diff --git a/src/Func.cpp b/src/Func.cpp
index a081116762df..23d03447ba28 100644
--- a/src/Func.cpp
+++ b/src/Func.cpp
@@ -3190,7 +3190,7 @@ Func define_base_case(const Internal::Function &func, const vector<Expr> &a, con
     // Reuse names of existing pure args
     for (size_t i = 0; i < a.size(); i++) {
         if (const Variable *v = a[i].as<Variable>()) {
-            if (!v->param.defined()) {
+            if (!v->param.defined() && !v->reduction_domain.defined()) {
                 pure_args[i] = Var(v->name);
             }
         } else {
diff --git a/test/correctness/CMakeLists.txt b/test/correctness/CMakeLists.txt
index a25b077a1abb..c6c90f833db0 100644
--- a/test/correctness/CMakeLists.txt
+++ b/test/correctness/CMakeLists.txt
@@ -180,6 +180,7 @@ tests(GROUPS correctness
       image_of_lists.cpp
       implicit_args.cpp
       implicit_args_tests.cpp
+      implicit_pure_def_with_rvar_args.cpp
       in_place.cpp
       indexing_access_undef.cpp
       infer_arguments.cpp
diff --git a/test/correctness/implicit_pure_def_with_rvar_args.cpp b/test/correctness/implicit_pure_def_with_rvar_args.cpp
new file mode 100644
index 000000000000..3449e0adadca
--- /dev/null
+++ b/test/correctness/implicit_pure_def_with_rvar_args.cpp
@@ -0,0 +1,97 @@
+#include "Halide.h"
+#include <cstdio>
+
+using namespace Halide;
+
+// Regression test for https://github.com/halide/Halide/issues/9102
+//
+// When a Func's first definition is an update that uses RVars directly
+// as LHS args (e.g. h(r.x) += ...), Halide auto-generates an implicit
+// pure definition. The pure dimension must not share a name with the
+// RVar, or bounds inference resolves the update's RVar loop bounds to
+// the pure dimension's (buffer-driven) bounds instead of the RDom's.
+
+int main(int argc, char **argv) {
+    Var x;
+
+    // Case 1: the original reproducer. vectorize(r.x) requires the RVar
+    // loop to have a constant extent; before the fix, bounds inference
+    // produced a symbolic extent from the output buffer and this
+    // schedule failed to compile.
+    {
+        RDom r(0, 16, 0, 8);
+        Func f{"f"}, g{"g"}, h{"h"};
+        f(x) = x + 1;
+        g(x) = 2 * x + 3;
+
+        h(r.x) += f(r.x + r.y) * g(r.y);
+
+        f.compute_root();
+        g.compute_root();
+        h.update().atomic().vectorize(r.x).unroll(r.y);
+
+        Buffer<int> out = h.realize({16});
+        for (int i = 0; i < 16; i++) {
+            int expected = 0;
+            for (int j = 0; j < 8; j++) {
+                expected += (i + j + 1) * (2 * j + 3);
+            }
+            if (out(i) != expected) {
+                printf("Case 1: out(%d) = %d, expected %d\n", i, out(i), expected);
+                return 1;
+            }
+        }
+    }
+
+    // Case 2: same computation, but with an explicit pure definition.
+    // This was the user's workaround; it must still give the same answer.
+    {
+        RDom r(0, 16, 0, 8);
+        Func f{"f2"}, g{"g2"}, h{"h2"};
+        f(x) = x + 1;
+        g(x) = 2 * x + 3;
+
+        h(x) = 0;
+        h(r.x) += f(r.x + r.y) * g(r.y);
+
+        f.compute_root();
+        g.compute_root();
+        h.update().atomic().vectorize(r.x).unroll(r.y);
+
+        Buffer<int> out = h.realize({16});
+        for (int i = 0; i < 16; i++) {
+            int expected = 0;
+            for (int j = 0; j < 8; j++) {
+                expected += (i + j + 1) * (2 * j + 3);
+            }
+            if (out(i) != expected) {
+                printf("Case 2: out(%d) = %d, expected %d\n", i, out(i), expected);
+                return 1;
+            }
+        }
+    }
+
+    // Case 3: RDom bounds narrower than the realized output. Exercises
+    // the underlying bounds bug directly (no vectorize needed): without
+    // a correct loop bound from the RDom, the update would write to
+    // indices outside the RDom, producing wrong values at the ends.
+    {
+        RDom r(2, 5);
+        Func h{"h3"};
+        h(r) += cast<int>(r) * 10;
+
+        h.update().vectorize(r, 4, TailStrategy::GuardWithIf);
+
+        Buffer<int> out = h.realize({10});
+        for (int i = 0; i < 10; i++) {
+            int expected = (i >= 2 && i < 7) ? i * 10 : 0;
+            if (out(i) != expected) {
+                printf("Case 3: out(%d) = %d, expected %d\n", i, out(i), expected);
+                return 1;
+            }
+        }
+    }
+
+    printf("Success!\n");
+    return 0;
+}