diff --git a/src/writer/hlsl/generator_impl.cc b/src/writer/hlsl/generator_impl.cc
index 372e9de5d4..3f03dc76bc 100644
--- a/src/writer/hlsl/generator_impl.cc
+++ b/src/writer/hlsl/generator_impl.cc
@@ -3127,6 +3127,11 @@ bool GeneratorImpl::EmitStructType(const sem::Struct* str) {
           }
           pre += mod;
 
+        } else if (deco->Is<ast::InvariantDecoration>()) {
+          // Note: `precise` is not exactly the same as `invariant`, but is
+          // stricter and therefore provides the necessary guarantees.
+          // See discussion here: https://github.com/gpuweb/gpuweb/issues/893
+          pre += "precise ";
         } else if (!deco->IsAnyOf<ast::StructMemberAlignDecoration,
                                   ast::StructMemberSizeDecoration>()) {
           TINT_ICE(Writer, diagnostics_)
diff --git a/test/shader_io/invariant.wgsl.expected.hlsl b/test/shader_io/invariant.wgsl.expected.hlsl
index f0fa6fe3a9..4597e8d10e 100644
--- a/test/shader_io/invariant.wgsl.expected.hlsl
+++ b/test/shader_io/invariant.wgsl.expected.hlsl
@@ -1,10 +1,8 @@
-SKIP: FAILED
-
-../../src/writer/hlsl/generator_impl.cc:3056 internal compiler error: unhandled struct member attribute: invariant
-********************************************************************
-*  The tint shader compiler has encountered an unexpected error.   *
-*                                                                  *
-*  Please help us fix this issue by submitting a bug report at     *
-*  crbug.com/tint with the source program that triggered the bug.  *
-********************************************************************
+struct tint_symbol {
+  precise float4 value : SV_Position;
+};
 
+tint_symbol main() {
+  const tint_symbol tint_symbol_1 = {float4(0.0f, 0.0f, 0.0f, 0.0f)};
+  return tint_symbol_1;
+}
diff --git a/test/shader_io/invariant_struct_member.wgsl.expected.hlsl b/test/shader_io/invariant_struct_member.wgsl.expected.hlsl
index f0fa6fe3a9..9090f0ed63 100644
--- a/test/shader_io/invariant_struct_member.wgsl.expected.hlsl
+++ b/test/shader_io/invariant_struct_member.wgsl.expected.hlsl
@@ -1,10 +1,12 @@
-SKIP: FAILED
-
-../../src/writer/hlsl/generator_impl.cc:3056 internal compiler error: unhandled struct member attribute: invariant
-********************************************************************
-*  The tint shader compiler has encountered an unexpected error.   *
-*                                                                  *
-*  Please help us fix this issue by submitting a bug report at     *
-*  crbug.com/tint with the source program that triggered the bug.  *
-********************************************************************
+struct Out {
+  float4 pos;
+};
+struct tint_symbol {
+  precise float4 pos : SV_Position;
+};
 
+tint_symbol main() {
+  const Out tint_symbol_1 = (Out)0;
+  const tint_symbol tint_symbol_2 = {tint_symbol_1.pos};
+  return tint_symbol_2;
+}