diff --git a/hist/hist/src/TH1.cxx b/hist/hist/src/TH1.cxx
index f4465a04f2862..371774ba27c25 100644
--- a/hist/hist/src/TH1.cxx
+++ b/hist/hist/src/TH1.cxx
@@ -2609,8 +2609,12 @@ Double_t TH1::ComputeIntegral(Bool_t onlyPositive, Option_t *option)
 
             if (onlyPositive && y < 0) {
                  Error("ComputeIntegral","Bin content is negative - return a NaN value");
-                 fIntegral[nbins] = TMath::QuietNaN();
-                 break;
+                 // Do not cache a partial integral: later rows could overwrite the
+                 // failure marker, and other consumers assume fIntegral is a valid CDF.
+                 // A subsequent request recomputes the integral and reports the error again.
+                 delete[] fIntegral;
+                 fIntegral = nullptr;
+                 return TMath::QuietNaN();
              }
             fIntegral[ibin] = fIntegral[ibin - 1] + y;
          }
@@ -5204,7 +5208,8 @@ Double_t TH1::GetRandom(TRandom *rng, Option_t *option) const
    }
    if (integral == 0) return 0;
    // return a NaN in case some bins have negative content
-   if (integral == TMath::QuietNaN() ) return TMath::QuietNaN();
+   if (std::isnan(integral))
+      return TMath::QuietNaN();
 
    Double_t r1 = (rng) ? rng->Rndm() : gRandom->Rndm();
    Int_t ibin = TMath::BinarySearch(nbinsx,fIntegral,r1);
diff --git a/hist/hist/src/TH2.cxx b/hist/hist/src/TH2.cxx
index dfd5df93f51be..22eb6630033e8 100644
--- a/hist/hist/src/TH2.cxx
+++ b/hist/hist/src/TH2.cxx
@@ -28,6 +28,7 @@
 #include "TVirtualHistPainter.h"
 #include "snprintf.h"
 
+#include <cmath>
 
 /** \addtogroup Histograms
 @{
@@ -765,7 +766,14 @@ void TH2::FillRandom(TH1 *h, Int_t ntimes, TRandom * rng)
       Error("FillRandom", "Histograms with different dimensions"); return;
    }
 
-   if (h->ComputeIntegral() == 0) return;
+   // Do not let GetRandom2 reuse an integral computed without the negative-bin check.
+   const Double_t integral = h->ComputeIntegral(true);
+   if (std::isnan(integral)) {
+      Error("FillRandom", "Histograms contains negative bins, does not represent probabilities");
+      return;
+   }
+   if (integral == 0)
+      return;
 
    Int_t loop;
    Double_t x,y;
@@ -1184,7 +1192,11 @@ void TH2::GetRandom2(Double_t &x, Double_t &y, TRandom *rng, Option_t *option)
    }
    if (integral == 0 ) { x = 0; y = 0; return;}
    // case histogram has negative bins
-   if (integral == TMath::QuietNaN() ) { x = TMath::QuietNaN(); y = TMath::QuietNaN(); return;}
+   if (std::isnan(integral)) {
+      x = TMath::QuietNaN();
+      y = TMath::QuietNaN();
+      return;
+   }
 
    if (!rng) rng = gRandom;
    Double_t r1 = rng->Rndm();
diff --git a/hist/hist/src/TH3.cxx b/hist/hist/src/TH3.cxx
index de7a3de5e0aa7..8858093efa83d 100644
--- a/hist/hist/src/TH3.cxx
+++ b/hist/hist/src/TH3.cxx
@@ -27,6 +27,7 @@
 
 #include <algorithm>
 #include <atomic>
+#include <cmath>
 #include <stdexcept>
 
 
@@ -959,7 +960,14 @@ void TH3::FillRandom(TH1 *h, Int_t ntimes, TRandom * rng)
       Error("FillRandom", "Histograms with different dimensions"); return;
    }
 
-   if (h->ComputeIntegral() == 0) return;
+   // Do not let GetRandom3 reuse an integral computed without the negative-bin check.
+   const Double_t integral = h->ComputeIntegral(true);
+   if (std::isnan(integral)) {
+      Error("FillRandom", "Histograms contains negative bins, does not represent probabilities");
+      return;
+   }
+   if (integral == 0)
+      return;
 
    TH3 *h3 = (TH3*)h;
    Int_t loop;
@@ -1302,7 +1310,12 @@ void TH3::GetRandom3(Double_t &x, Double_t &y, Double_t &z, TRandom *rng, Option
    }
    if (integral == 0 ) { x = 0; y = 0; z = 0; return;}
    // case histogram has negative bins
-   if (integral == TMath::QuietNaN() ) { x = TMath::QuietNaN(); y = TMath::QuietNaN(); z = TMath::QuietNaN(); return;}
+   if (std::isnan(integral)) {
+      x = TMath::QuietNaN();
+      y = TMath::QuietNaN();
+      z = TMath::QuietNaN();
+      return;
+   }
 
    if (!rng) rng = gRandom;
    Double_t r1 = rng->Rndm();
diff --git a/hist/hist/test/test_TH1.cxx b/hist/hist/test/test_TH1.cxx
index dffcd66d679bb..8cceb9f7632d6 100644
--- a/hist/hist/test/test_TH1.cxx
+++ b/hist/hist/test/test_TH1.cxx
@@ -4,9 +4,11 @@
 #include "TH2.h"
 #include "TH3.h"
 #include "TH1F.h"
+#include "TH2Poly.h"
 #include "THLimitsFinder.h"
 #include "TDirectory.h"
 #include "TList.h"
+#include "TRandom3.h"
 #include "TROOT.h"
 
 #include <cmath>
@@ -562,3 +564,146 @@ TEST(TH1, GetCumulativeErrors)
          }
    }
 }
+
+namespace {
+
+class TH1DIntegralAccess : public TH1D {
+public:
+   using TH1D::TH1D;
+   bool HasCachedIntegral() const { return fIntegral != nullptr; }
+};
+
+} // namespace
+
+TEST(TH1, GetRandomNegativeBin)
+{
+   ROOT::TestSupport::CheckDiagsRAII diags;
+   diags.requiredDiag(kError, "TH1D::ComputeIntegral", "Bin content is negative - return a NaN value");
+
+   TH1DIntegralAccess h("hNegRandom", "", 2, 0., 2.);
+   h.SetBinContent(1, 1.);
+   h.SetBinContent(2, -0.25);
+
+   TRandom3 rng(1);
+   TRandom3 referenceRng(1);
+   EXPECT_TRUE(std::isnan(h.GetRandom(&rng)));
+   EXPECT_FALSE(h.HasCachedIntegral());
+   EXPECT_DOUBLE_EQ(rng.Rndm(), referenceRng.Rndm());
+}
+
+TEST(TH2, GetRandom2NegativeBin)
+{
+   ROOT::TestSupport::CheckDiagsRAII diags;
+   diags.requiredDiag(kError, "TH2D::ComputeIntegral", "Bin content is negative - return a NaN value");
+
+   TH2D h("hNegRandom2", "", 2, 0., 2., 2, 0., 2.);
+   h.SetBinContent(1, 1, 1.);
+   h.SetBinContent(2, 1, -0.25);
+   h.SetBinContent(1, 2, 1.);
+   h.SetBinContent(2, 2, 1.);
+
+   TRandom3 rng(1);
+   TRandom3 referenceRng(1);
+   double x = 0., y = 0.;
+   h.GetRandom2(x, y, &rng);
+   EXPECT_TRUE(std::isnan(x));
+   EXPECT_TRUE(std::isnan(y));
+   EXPECT_DOUBLE_EQ(rng.Rndm(), referenceRng.Rndm());
+}
+
+TEST(TH3, GetRandom3NegativeBin)
+{
+   ROOT::TestSupport::CheckDiagsRAII diags;
+   diags.requiredDiag(kError, "TH3D::ComputeIntegral", "Bin content is negative - return a NaN value");
+
+   TH3D h("hNegRandom3", "", 2, 0., 2., 2, 0., 2., 2, 0., 2.);
+   h.SetBinContent(1, 1, 1, 1.);
+   h.SetBinContent(2, 2, 2, -0.25);
+
+   TRandom3 rng(1);
+   TRandom3 referenceRng(1);
+   double x = 0., y = 0., z = 0.;
+   h.GetRandom3(x, y, z, &rng);
+   EXPECT_TRUE(std::isnan(x));
+   EXPECT_TRUE(std::isnan(y));
+   EXPECT_TRUE(std::isnan(z));
+   EXPECT_DOUBLE_EQ(rng.Rndm(), referenceRng.Rndm());
+}
+
+TEST(TH2, FillRandomNegativeBin)
+{
+   ROOT::TestSupport::CheckDiagsRAII diags;
+   diags.requiredDiag(kError, "TH2D::ComputeIntegral", "Bin content is negative - return a NaN value");
+   diags.requiredDiag(kError, "TH2D::FillRandom",
+                      "Histograms contains negative bins, does not represent probabilities");
+
+   TH2D src("hFillRandom2Src", "", 2, 0., 2., 2, 0., 2.);
+   src.SetBinContent(1, 1, 1.);
+   src.SetBinContent(2, 1, -0.25);
+   src.SetBinContent(1, 2, 1.);
+   src.SetBinContent(2, 2, 1.);
+
+   TH2D dest("hFillRandom2Dest", "", 2, 0., 2., 2, 0., 2.);
+   TRandom3 rng(1);
+   dest.FillRandom(&src, 1, &rng);
+   EXPECT_EQ(dest.GetEntries(), 0.);
+}
+
+TEST(TH3, FillRandomNegativeBin)
+{
+   ROOT::TestSupport::CheckDiagsRAII diags;
+   diags.requiredDiag(kError, "TH3D::ComputeIntegral", "Bin content is negative - return a NaN value");
+   diags.requiredDiag(kError, "TH3D::FillRandom",
+                      "Histograms contains negative bins, does not represent probabilities");
+
+   TH3D src("hFillRandom3Src", "", 2, 0., 2., 2, 0., 2., 2, 0., 2.);
+   src.SetBinContent(1, 1, 1, 1.);
+   src.SetBinContent(2, 2, 2, -0.25);
+
+   TH3D dest("hFillRandom3Dest", "", 2, 0., 2., 2, 0., 2., 2, 0., 2.);
+   TRandom3 rng(1);
+   dest.FillRandom(&src, 1, &rng);
+   EXPECT_EQ(dest.GetEntries(), 0.);
+}
+
+TEST(TH2, FillRandomPositiveBins)
+{
+   ROOT::TestSupport::CheckDiagsRAII diags;
+   TRandom3 rng(1);
+
+   TH2D src("hFillRandom2PositiveSrc", "", 1, 0., 1., 1, 0., 1.);
+   src.SetBinContent(1, 1, 1.);
+   TH2D dest("hFillRandom2PositiveDest", "", 1, 0., 1., 1, 0., 1.);
+   dest.FillRandom(&src, 1, &rng);
+   EXPECT_EQ(dest.GetEntries(), 1.);
+   EXPECT_EQ(dest.Integral(), 1.);
+}
+
+TEST(TH3, FillRandomPositiveBins)
+{
+   ROOT::TestSupport::CheckDiagsRAII diags;
+   TRandom3 rng(1);
+
+   TH3D src("hFillRandom3PositiveSrc", "", 1, 0., 1., 1, 0., 1., 1, 0., 1.);
+   src.SetBinContent(1, 1, 1, 1.);
+   TH3D dest("hFillRandom3PositiveDest", "", 1, 0., 1., 1, 0., 1., 1, 0., 1.);
+   dest.FillRandom(&src, 1, &rng);
+   EXPECT_EQ(dest.GetEntries(), 1.);
+   EXPECT_EQ(dest.Integral(), 1.);
+}
+
+TEST(TH2Poly, GetRandom2NotImplemented)
+{
+   ROOT::TestSupport::CheckDiagsRAII diags;
+   diags.requiredDiag(kError, "TH2Poly::ComputeIntegral", "Not implemented for TH2Poly");
+
+   TH2Poly h("hPolyRandom", "", 0., 2., 0., 2.);
+   h.AddBin(0., 0., 1., 1.);
+   h.AddBin(1., 1., 2., 2.);
+
+   TRandom3 rng(1);
+   double x = 0., y = 0.;
+   h.GetRandom2(x, y, &rng);
+   EXPECT_TRUE(std::isnan(x));
+   EXPECT_TRUE(std::isnan(y));
+}