diff --git a/api/utils/grpc/interceptors/errors.go b/api/utils/grpc/interceptors/errors.go
index e765cc10a94a0..3b9e834b60c18 100644
--- a/api/utils/grpc/interceptors/errors.go
+++ b/api/utils/grpc/interceptors/errors.go
@@ -50,22 +50,24 @@ type grpcClientStreamWrapper struct {
 
 // SendMsg wraps around ClientStream.SendMsg
 func (s *grpcClientStreamWrapper) SendMsg(m interface{}) error {
-	if err := s.ClientStream.SendMsg(m); err != nil {
-		return &RemoteError{Err: trace.Unwrap(trail.FromGRPC(s.ClientStream.SendMsg(m)))}
-	}
-	return nil
+	return wrapStreamErr(s.ClientStream.SendMsg(m))
 }
 
 // RecvMsg wraps around ClientStream.RecvMsg
 func (s *grpcClientStreamWrapper) RecvMsg(m interface{}) error {
-	switch err := s.ClientStream.RecvMsg(m); {
+	return wrapStreamErr(s.ClientStream.RecvMsg(m))
+}
+
+func wrapStreamErr(err error) error {
+	switch {
+	case err == nil:
+		return nil
 	case errors.Is(err, io.EOF):
 		// Do not wrap io.EOF errors, they are often used as stop guards for streams.
 		return err
-	case err != nil:
-		return &RemoteError{Err: trace.Unwrap(trail.FromGRPC(s.ClientStream.RecvMsg(m)))}
+	default:
+		return &RemoteError{Err: trace.Unwrap(trail.FromGRPC(err))}
 	}
-	return nil
 }
 
 // GRPCServerUnaryErrorInterceptor is a gRPC unary server interceptor that
diff --git a/api/utils/grpc/interceptors/errors_test.go b/api/utils/grpc/interceptors/errors_test.go
index ffa0d28356e5c..3e01ffca507ff 100644
--- a/api/utils/grpc/interceptors/errors_test.go
+++ b/api/utils/grpc/interceptors/errors_test.go
@@ -16,10 +16,10 @@ package interceptors_test
 
 import (
 	"context"
-	"errors"
 	"io"
 	"net"
 	"testing"
+	"time"
 
 	"github.com/gravitational/trace"
 	"github.com/stretchr/testify/assert"
@@ -88,15 +88,19 @@ func TestGRPCErrorWrapping(t *testing.T) {
 		stream, err := client.AddMFADevice(context.Background())
 		require.NoError(t, err)
 
+		// Give the server time to close the stream. This allows us to more
+		// consistently hit the io.EOF error.
+		time.Sleep(100 * time.Millisecond)
+
 		//nolint:staticcheck // SA1019. The specific stream used here doesn't matter.
 		sendErr := stream.Send(&proto.AddMFADeviceRequest{})
 
-		// io.EOF means the server closed the stream, which can
-		// happen depending in timing. In either case, it is
-		// still safe to recv from the stream and check for
+		// Expect either a success (unlikely because of the Sleep) or an unwrapped
+		// io.EOF error (meaning the server errored and closed the stream).
+		// In either case, it is still safe to recv from the stream and check for
 		// the already exists error.
-		if sendErr != nil && !errors.Is(sendErr, io.EOF) {
-			t.Fatalf("Unexpected error: %v", sendErr)
+		if sendErr != nil && sendErr != io.EOF /* == error comparison on purpose! */ {
+			t.Fatalf("Unexpected error: %q (%T)", sendErr, sendErr)
 		}
 
 		_, err = stream.Recv()