diff --git a/packages/angular_devkit/schematics/src/tree/host-tree.ts b/packages/angular_devkit/schematics/src/tree/host-tree.ts
index fbd626c6a8d2..eab9c9d3809c 100644
--- a/packages/angular_devkit/schematics/src/tree/host-tree.ts
+++ b/packages/angular_devkit/schematics/src/tree/host-tree.ts
@@ -341,7 +341,9 @@ export class HostTree implements Tree {
         throw new ContentHasMutatedException(path);
       } else {
         const newContent = record.apply(entry.content);
-        this.overwrite(path, newContent);
+        if (!newContent.equals(entry.content)) {
+          this.overwrite(path, newContent);
+        }
       }
     } else {
       throw new InvalidUpdateRecordException();
diff --git a/packages/schematics/angular/migrations/update-9/add-tslib.ts b/packages/schematics/angular/migrations/update-9/add-tslib.ts
index ad562fcb41c0..ca4eca9fa776 100644
--- a/packages/schematics/angular/migrations/update-9/add-tslib.ts
+++ b/packages/schematics/angular/migrations/update-9/add-tslib.ts
@@ -6,16 +6,22 @@
  * found in the LICENSE file at https://angular.io/license
  */
 import { Rule } from '@angular-devkit/schematics';
-import { NodeDependencyType, addPackageJsonDependency, removePackageJsonDependency } from '../../utility/dependencies';
+import { NodeDependencyType, addPackageJsonDependency, getPackageJsonDependency, removePackageJsonDependency } from '../../utility/dependencies';
 import { latestVersions } from '../../utility/latest-versions';
 
 export function addTsLib(): Rule {
   return host => {
-    removePackageJsonDependency(host, 'tslib');
+    const tslibDep = getPackageJsonDependency(host, 'tslib');
+
+    if (tslibDep && tslibDep.type !== NodeDependencyType.Default) {
+      removePackageJsonDependency(host, 'tslib');
+    }
+
     addPackageJsonDependency(host, {
-        name: 'tslib',
-        version: latestVersions.TsLib,
-        type: NodeDependencyType.Default,
+      name: 'tslib',
+      version: latestVersions.TsLib,
+      type: NodeDependencyType.Default,
+      overwrite: true,
     });
   };
 }