diff --git a/roofit/roofitcore/src/TestStatistics/RooUnbinnedL.cxx b/roofit/roofitcore/src/TestStatistics/RooUnbinnedL.cxx
index 7e8fd790e0522..e342b3411c1fe 100644
--- a/roofit/roofitcore/src/TestStatistics/RooUnbinnedL.cxx
+++ b/roofit/roofitcore/src/TestStatistics/RooUnbinnedL.cxx
@@ -62,8 +62,12 @@ RooUnbinnedL::RooUnbinnedL(RooAbsPdf *pdf, RooAbsData *data, RooAbsL::Extended e
    if (evalBackend.value() != RooFit::EvalBackend::Value::Legacy) {
       evaluator_ = std::make_unique<RooFit::Evaluator>(*pdf_, evalBackend.value() == RooFit::EvalBackend::Value::Cuda);
       std::stack<std::vector<double>>{}.swap(_vectorBuffers);
+      // Zero-weight events must not be skipped here: the probabilities from
+      // the evaluator are indexed by the original event indices, aligned with
+      // the weights obtained from RooAbsData::getWeightBatch(). Events with
+      // zero weight are skipped in the summation instead.
       auto dataSpans =
-         RooFit::BatchModeDataHelpers::getDataSpans(*data, "", nullptr, /*skipZeroWeights=*/true,
+         RooFit::BatchModeDataHelpers::getDataSpans(*data, "", nullptr, /*skipZeroWeights=*/false,
                                                     /*takeGlobalObservablesFromData=*/false, _vectorBuffers);
       for (auto const &item : dataSpans) {
          evaluator_->setInput(item.first->GetName(), item.second, false);
diff --git a/roofit/roofitcore/test/TestStatistics/testRooAbsL.cxx b/roofit/roofitcore/test/TestStatistics/testRooAbsL.cxx
index 851796f51d510..119294820d838 100644
--- a/roofit/roofitcore/test/TestStatistics/testRooAbsL.cxx
+++ b/roofit/roofitcore/test/TestStatistics/testRooAbsL.cxx
@@ -28,6 +28,7 @@
 
 #include "Math/Util.h" // KahanSum
 
+#include <cmath>     // isnan
 #include <stdexcept> // runtime_error
 
 #include "gtest/gtest.h"
@@ -304,6 +305,47 @@ TEST_F(SimBinnedConstrainedTest, SubEventSections)
    EXPECT_DOUBLE_EQ(whole.Sum(), thrice_N_events_total_parts.Sum());
 }
 
+TEST_F(RooAbsLTest, ZeroWeightsWithBatchEvaluator)
+{
+   // The probabilities returned by the RooFit::Evaluator are indexed by the
+   // original event indices, aligned with the weights that are obtained from
+   // RooAbsData::getWeightBatch(). This test checks that zero-weight events
+   // (e.g. empty bins of a binned dataset) don't spoil this alignment, which
+   // resulted in NaN likelihood values in the past.
+
+   w.factory("Gaussian::g(x[-10,10],mu[0,-5,5],sigma[1,0.1,10])");
+   w.var("x")->setBins(40);
+   pdf = w.pdf("g");
+   data = std::unique_ptr<RooDataHist>{pdf->generateBinned(*w.var("x"), 100)};
+
+   // The whole point of this test is to have zero-weight events in the
+   // dataset, so make sure the empty tail bins are really there.
+   std::size_t nZeroWeight = 0;
+   for (int i = 0; i < data->numEntries(); ++i) {
+      data->get(i);
+      nZeroWeight += (data->weight() == 0.);
+   }
+   ASSERT_GT(nZeroWeight, 0);
+
+   // Compute the reference NLL value by hand, skipping zero-weight events.
+   RooArgSet normSet{*w.var("x")};
+   ROOT::Math::KahanSum<double> refNll;
+   for (int i = 0; i < data->numEntries(); ++i) {
+      w.var("x")->setVal(data->get(i)->getRealValue("x"));
+      if (data->weight() == 0.)
+         continue;
+      refNll += -data->weight() * std::log(pdf->getVal(normSet));
+   }
+
+   likelihood = std::make_shared<RooFit::TestStatistics::RooUnbinnedL>(
+      pdf, data.get(), RooFit::TestStatistics::RooAbsL::Extended::Auto, RooFit::EvalBackend::Cpu());
+
+   const double nllVal = likelihood->evaluatePartition({0, 1}, 0, 0).Sum();
+
+   EXPECT_FALSE(std::isnan(nllVal));
+   EXPECT_NEAR(nllVal, refNll.Sum(), 1e-8 * std::abs(refNll.Sum()));
+}
+
 TEST_F(RooAbsLTest, VSRooNLLVar)
 {
    // compare the value of the likelihood to that generated by a similarly configured RooNLLVar