diff --git a/modules/@angular/router/src/apply_redirects.ts b/modules/@angular/router/src/apply_redirects.ts
index b66afa0a5f..164a8af1bd 100644
--- a/modules/@angular/router/src/apply_redirects.ts
+++ b/modules/@angular/router/src/apply_redirects.ts
@@ -146,13 +146,22 @@ class ApplyRedirects {
     const first$ = first.call(concattedProcessedRoutes$, (s: any) => !!s);
     return _catch.call(first$, (e: any, _: any): Observable<UrlSegmentGroup> => {
       if (e instanceof EmptyError) {
-        throw new NoMatch(segmentGroup);
+        if (this.noLeftoversInUrl(segmentGroup, segments, outlet)) {
+          return of (new UrlSegmentGroup([], {}));
+        } else {
+          throw new NoMatch(segmentGroup);
+        }
       } else {
         throw e;
       }
     });
   }
 
+  private noLeftoversInUrl(segmentGroup: UrlSegmentGroup, segments: UrlSegment[], outlet: string):
+      boolean {
+    return segments.length === 0 && !segmentGroup.children[outlet];
+  }
+
   private expandSegmentAgainstRoute(
       injector: Injector, segmentGroup: UrlSegmentGroup, routes: Route[], route: Route,
       paths: UrlSegment[], outlet: string, allowRedirects: boolean): Observable<UrlSegmentGroup> {
diff --git a/modules/@angular/router/src/recognize.ts b/modules/@angular/router/src/recognize.ts
index 6e3c7a01de..4fb4fed459 100644
--- a/modules/@angular/router/src/recognize.ts
+++ b/modules/@angular/router/src/recognize.ts
@@ -90,7 +90,16 @@ class Recognizer {
         if (!(e instanceof NoMatch)) throw e;
       }
     }
-    throw new NoMatch();
+    if (this.noLeftoversInUrl(segmentGroup, segments, outlet)) {
+      return [];
+    } else {
+      throw new NoMatch();
+    }
+  }
+
+  private noLeftoversInUrl(segmentGroup: UrlSegmentGroup, segments: UrlSegment[], outlet: string):
+      boolean {
+    return segments.length === 0 && !segmentGroup.children[outlet];
   }
 
   processSegmentAgainstRoute(
diff --git a/modules/@angular/router/test/apply_redirects.spec.ts b/modules/@angular/router/test/apply_redirects.spec.ts
index c7a2c3a38b..ef96cf017e 100644
--- a/modules/@angular/router/test/apply_redirects.spec.ts
+++ b/modules/@angular/router/test/apply_redirects.spec.ts
@@ -515,6 +515,37 @@ describe('applyRedirects', () => {
       });
     });
   });
+
+  describe('empty URL leftovers', () => {
+    it('should not error when no children matching and no url is left', () => {
+      checkRedirect(
+          [{path: 'a', component: ComponentA, children: [{path: 'b', component: ComponentB}]}],
+          '/a', (t: UrlTree) => { compareTrees(t, tree('a')); });
+    });
+
+    it('should not error when no children matching and no url is left (aux routes)', () => {
+      checkRedirect(
+          [{
+            path: 'a',
+            component: ComponentA,
+            children: [
+              {path: 'b', component: ComponentB},
+              {path: '', redirectTo: 'c', outlet: 'aux'},
+              {path: 'c', component: ComponentC, outlet: 'aux'},
+            ]
+          }],
+          '/a', (t: UrlTree) => { compareTrees(t, tree('a/(aux:c)')); });
+    });
+
+    it('should error when no children matching and some url is left', () => {
+      applyRedirects(
+          null, null, tree('/a/c'),
+          [{path: 'a', component: ComponentA, children: [{path: 'b', component: ComponentB}]}])
+          .subscribe(
+              (_) => { throw 'Should not be reached'; },
+              e => { expect(e.message).toEqual('Cannot match any routes. URL Segment: \'a/c\''); });
+    });
+  });
 });
 
 function checkRedirect(config: Routes, url: string, callback: any): void {
diff --git a/modules/@angular/router/test/integration.spec.ts b/modules/@angular/router/test/integration.spec.ts
index 0b02b88160..ad1867be3c 100644
--- a/modules/@angular/router/test/integration.spec.ts
+++ b/modules/@angular/router/test/integration.spec.ts
@@ -22,11 +22,8 @@ import {RouterTestingModule, SpyNgModuleFactoryLoader} from '../testing';
 describe('Integration', () => {
   beforeEach(() => {
     TestBed.configureTestingModule({
-      imports: [
-        RouterTestingModule.withRoutes(
-            [{path: '', component: BlankCmp}, {path: 'simple', component: SimpleCmp}]),
-        TestModule
-      ]
+      imports:
+          [RouterTestingModule.withRoutes([{path: 'simple', component: SimpleCmp}]), TestModule]
     });
   });
 
@@ -165,6 +162,29 @@ describe('Integration', () => {
        })));
   });
 
+  it('should not error when no url left and no children are matching',
+     fakeAsync(inject([Router, Location], (router: Router, location: Location) => {
+       const fixture = createRoot(router, RootCmp);
+
+       router.resetConfig([{
+         path: 'team/:id',
+         component: TeamCmp,
+         children: [{path: 'simple', component: SimpleCmp}]
+       }]);
+
+       router.navigateByUrl('/team/33/simple');
+       advance(fixture);
+
+       expect(location.path()).toEqual('/team/33/simple');
+       expect(fixture.nativeElement).toHaveText('team 33 [ simple, right:  ]');
+
+       router.navigateByUrl('/team/33');
+       advance(fixture);
+
+       expect(location.path()).toEqual('/team/33');
+       expect(fixture.nativeElement).toHaveText('team 33 [ , right:  ]');
+     })));
+
   it('should work when an outlet is in an ngIf',
      fakeAsync(inject([Router, Location], (router: Router, location: Location) => {
        const fixture = createRoot(router, RootCmp);
@@ -711,13 +731,13 @@ describe('Integration', () => {
        expect(cmp.activations.length).toEqual(1);
        expect(cmp.activations[0] instanceof BlankCmp).toBe(true);
 
-       router.navigateByUrl('/simple');
+       router.navigateByUrl('/simple').catch(e => console.log(e));
        advance(fixture);
 
        expect(cmp.activations.length).toEqual(2);
        expect(cmp.activations[1] instanceof SimpleCmp).toBe(true);
-       expect(cmp.deactivations.length).toEqual(2);
-       expect(cmp.deactivations[1] instanceof BlankCmp).toBe(true);
+       expect(cmp.deactivations.length).toEqual(1);
+       expect(cmp.deactivations[0] instanceof BlankCmp).toBe(true);
      }));
 
   it('should update url and router state before activating components',
diff --git a/modules/@angular/router/test/recognize.spec.ts b/modules/@angular/router/test/recognize.spec.ts
index 43408f4925..e822d13a52 100644
--- a/modules/@angular/router/test/recognize.spec.ts
+++ b/modules/@angular/router/test/recognize.spec.ts
@@ -608,6 +608,34 @@ describe('recognize', () => {
     });
   });
 
+  describe('empty URL leftovers', () => {
+    it('should not throw when no children matching', () => {
+      checkRecognize(
+          [{path: 'a', component: ComponentA, children: [{path: 'b', component: ComponentB}]}],
+          '/a', (s: RouterStateSnapshot) => {
+            const a = s.firstChild(s.root);
+            checkActivatedRoute(a, 'a', {}, ComponentA);
+          });
+    });
+
+    it('should not throw when no children matching (aux routes)', () => {
+      checkRecognize(
+          [{
+            path: 'a',
+            component: ComponentA,
+            children: [
+              {path: 'b', component: ComponentB},
+              {path: '', component: ComponentC, outlet: 'aux'},
+            ]
+          }],
+          '/a', (s: RouterStateSnapshot) => {
+            const a = s.firstChild(s.root);
+            checkActivatedRoute(a, 'a', {}, ComponentA);
+            checkActivatedRoute(a.children[0], '', {}, ComponentC, 'aux');
+          });
+    });
+  });
+
   describe('query parameters', () => {
     it('should support query params', () => {
       const config = [{path: 'a', component: ComponentA}];