diff --git a/.changelog/4186.txt b/.changelog/4186.txt
new file mode 100644
index 0000000000..711d083111
--- /dev/null
+++ b/.changelog/4186.txt
@@ -0,0 +1,3 @@
+```release-note:enhancement
+run: patched `google_cloud_run_service` to suppress Google generated annotations
+```
diff --git a/google-beta/resource_cloud_run_service.go b/google-beta/resource_cloud_run_service.go
index a92b290a02..b3ab732f60 100644
--- a/google-beta/resource_cloud_run_service.go
+++ b/google-beta/resource_cloud_run_service.go
@@ -20,6 +20,7 @@ import (
 	"log"
 	"reflect"
 	"strconv"
+	"strings"
 	"time"
 
 	"github.com/hashicorp/terraform-plugin-sdk/v2/helper/schema"
@@ -34,6 +35,23 @@ func revisionNameCustomizeDiff(_ context.Context, diff *schema.ResourceDiff, v i
 	return nil
 }
 
+const cloudRunGoogleProvidedAnnotation = "serving.knative.dev"
+
+func cloudrunAnnotationDiffSuppress(k, old, new string, d *schema.ResourceData) bool {
+	// Suppress diffs for the annotations provided by Google
+	if strings.Contains(k, cloudRunGoogleProvidedAnnotation) && new == "" {
+		return true
+	}
+
+	// Let diff be determined by annotations (above)
+	if strings.Contains(k, "annotations.%") {
+		return true
+	}
+
+	// For other keys, don't suppress diff.
+	return false
+}
+
 func resourceCloudRunService() *schema.Resource {
 	return &schema.Resource{
 		Create: resourceCloudRunServiceCreate,
@@ -485,9 +503,10 @@ and annotations.`,
 				Elem: &schema.Resource{
 					Schema: map[string]*schema.Schema{
 						"annotations": {
-							Type:     schema.TypeMap,
-							Computed: true,
-							Optional: true,
+							Type:             schema.TypeMap,
+							Computed:         true,
+							Optional:         true,
+							DiffSuppressFunc: cloudrunAnnotationDiffSuppress,
 							Description: `Annotations is a key value map stored with a resource that
 may be set by external tools to store and retrieve arbitrary metadata. More
 info: http://kubernetes.io/docs/user-guide/annotations`,
diff --git a/google-beta/resource_cloud_run_service_generated_test.go b/google-beta/resource_cloud_run_service_generated_test.go
index d1ec7957c8..c114590c47 100644
--- a/google-beta/resource_cloud_run_service_generated_test.go
+++ b/google-beta/resource_cloud_run_service_generated_test.go
@@ -254,6 +254,12 @@ resource "google_cloud_run_service" "default" {
     }
   }
 
+  metadata {
+    annotations = {
+      generated-by = "magic-modules"
+    }
+  }
+
   traffic {
     percent         = 100
     latest_revision = true
diff --git a/website/docs/r/cloud_run_domain_mapping.html.markdown b/website/docs/r/cloud_run_domain_mapping.html.markdown
index f1e433cc18..80a7ec934b 100644
--- a/website/docs/r/cloud_run_domain_mapping.html.markdown
+++ b/website/docs/r/cloud_run_domain_mapping.html.markdown
@@ -27,7 +27,7 @@ Resource to hold the state and status of a user's domain mapping.
 
 To get more information about DomainMapping, see:
 
-* [API documentation](https://cloud.google.com/run/docs/reference/rest/v1alpha1/projects.locations.domainmappings)
+* [API documentation](https://cloud.google.com/run/docs/reference/rest/v1/projects.locations.domainmappings)
 * How-to Guides
     * [Official Documentation](https://cloud.google.com/run/docs/mapping-custom-domains)
 
diff --git a/website/docs/r/cloud_run_service.html.markdown b/website/docs/r/cloud_run_service.html.markdown
index 11c82e2df4..a4d6da8496 100644
--- a/website/docs/r/cloud_run_service.html.markdown
+++ b/website/docs/r/cloud_run_service.html.markdown
@@ -180,6 +180,12 @@ resource "google_cloud_run_service" "default" {
     }
   }
 
+  metadata {
+    annotations = {
+      generated-by = "magic-modules"
+    }
+  }
+
   traffic {
     percent         = 100
     latest_revision = true