diff --git a/kernel/bpf/verifier.c b/kernel/bpf/verifier.c
index 9c6ad157a61e..b71c5274b3dc 100644
--- a/kernel/bpf/verifier.c
+++ b/kernel/bpf/verifier.c
@@ -4708,8 +4708,15 @@ static int check_map_kptr_access(struct bpf_verifier_env *env,
 			return ret;
 	} else if (class == BPF_STX) {
 		val_reg = reg_state(env, value_regno);
-		if (!bpf_register_is_null(val_reg) &&
-		    map_kptr_match_type(env, kptr_field, val_reg, value_regno))
+		if (bpf_register_is_null(val_reg)) {
+			/*
+			 * This store is valid only because the scalar is known to be
+			 * zero. Mark it precise so another scalar cannot be pruned
+			 * against this state.
+			 */
+			return mark_chain_precision(env, value_regno);
+		}
+		if (map_kptr_match_type(env, kptr_field, val_reg, value_regno))
 			return -EACCES;
 	} else if (class == BPF_ST) {
 		if (insn->imm) {