diff --git a/src/cdk/drag-drop/directives/drag.spec.ts b/src/cdk/drag-drop/directives/drag.spec.ts
index 80eab4e8f871..5ed0b9566180 100644
--- a/src/cdk/drag-drop/directives/drag.spec.ts
+++ b/src/cdk/drag-drop/directives/drag.spec.ts
@@ -691,7 +691,7 @@ describe('CdkDrag', () => {
       expect(styles.touchAction || (styles as any).webkitUserDrag).toBeFalsy();
     }));
 
-    it('should stop propagation for the drag sequence start event', fakeAsync(() => {
+    it('should not stop propagation for the drag sequence start event by default', fakeAsync(() => {
       const fixture = createComponent(StandaloneDraggable);
       fixture.detectChanges();
       const dragElement = fixture.componentInstance.dragElement.nativeElement;
@@ -702,7 +702,7 @@ describe('CdkDrag', () => {
       dispatchEvent(dragElement, event);
       fixture.detectChanges();
 
-      expect(event.stopPropagation).toHaveBeenCalled();
+      expect(event.stopPropagation).not.toHaveBeenCalled();
     }));
 
     it('should not throw if destroyed before the first change detection run', fakeAsync(() => {
@@ -5486,7 +5486,6 @@ describe('CdkDrag', () => {
 
   describe('with nested drags', () => {
     it('should not move draggable container when dragging child (multitouch)', fakeAsync(() => {
-
       const fixture = createComponent(NestedDragsComponent, [], 10);
       fixture.detectChanges();
 
@@ -5534,7 +5533,20 @@ describe('CdkDrag', () => {
           .toHaveBeenCalledTimes(containerDragMovedCount);
       expect(fixture.componentInstance.containerDragReleasedSpy)
           .toHaveBeenCalledTimes(containerDragReleasedCount);
+    }));
+
+    it('should stop event propagation when dragging a nested item', fakeAsync(() => {
+      const fixture = createComponent(NestedDragsComponent);
+      fixture.detectChanges();
+      const dragElement = fixture.componentInstance.item.nativeElement;
+
+      const event = createMouseEvent('mousedown');
+      spyOn(event, 'stopPropagation').and.callThrough();
+
+      dispatchEvent(dragElement, event);
+      fixture.detectChanges();
 
+      expect(event.stopPropagation).toHaveBeenCalled();
     }));
   });
 });
diff --git a/src/cdk/drag-drop/directives/drag.ts b/src/cdk/drag-drop/directives/drag.ts
index 8884997743b1..312a09edfb40 100644
--- a/src/cdk/drag-drop/directives/drag.ts
+++ b/src/cdk/drag-drop/directives/drag.ts
@@ -192,13 +192,15 @@ export class CdkDrag<T = any> implements AfterViewInit, OnChanges, OnDestroy {
       @Optional() @Inject(CDK_DRAG_CONFIG) config: DragDropConfig,
       @Optional() private _dir: Directionality, dragDrop: DragDrop,
       private _changeDetectorRef: ChangeDetectorRef,
-      @Optional() @Self() @Inject(CDK_DRAG_HANDLE) private _selfHandle?: CdkDragHandle) {
+      @Optional() @Self() @Inject(CDK_DRAG_HANDLE) private _selfHandle?: CdkDragHandle,
+      @Optional() @SkipSelf() @Inject(CDK_DRAG_PARENT) parentDrag?: CdkDrag) {
     this._dragRef = dragDrop.createDrag(element, {
       dragStartThreshold: config && config.dragStartThreshold != null ?
           config.dragStartThreshold : 5,
       pointerDirectionChangeThreshold: config && config.pointerDirectionChangeThreshold != null ?
           config.pointerDirectionChangeThreshold : 5,
-      zIndex: config?.zIndex
+      zIndex: config?.zIndex,
+      parentDragRef: parentDrag?._dragRef
     });
     this._dragRef.data = this;
 
diff --git a/src/cdk/drag-drop/drag-ref.ts b/src/cdk/drag-drop/drag-ref.ts
index da18f013d7dd..3cb0d626c522 100644
--- a/src/cdk/drag-drop/drag-ref.ts
+++ b/src/cdk/drag-drop/drag-ref.ts
@@ -36,6 +36,9 @@ export interface DragRefConfig {
 
   /** `z-index` for the absolutely-positioned elements that are created by the drag item. */
   zIndex?: number;
+
+  /** Ref that the current drag item is nested in. */
+  parentDragRef?: DragRef;
 }
 
 /** Options that can be used to bind a passive event listener. */
@@ -783,10 +786,11 @@ export class DragRef<T = any> {
    * @param event Browser event object that started the sequence.
    */
   private _initializeDragSequence(referenceElement: HTMLElement, event: MouseEvent | TouchEvent) {
-    // Always stop propagation for the event that initializes
-    // the dragging sequence, in order to prevent it from potentially
-    // starting another sequence for a draggable parent somewhere up the DOM tree.
-    event.stopPropagation();
+    // Stop propagation if the item is inside another
+    // draggable so we don't start multiple drag sequences.
+    if (this._config.parentDragRef) {
+      event.stopPropagation();
+    }
 
     const isDragging = this.isDragging();
     const isTouchSequence = isTouchEvent(event);
diff --git a/tools/public_api_guard/cdk/drag-drop.d.ts b/tools/public_api_guard/cdk/drag-drop.d.ts
index 7422c8819f87..03e7c1c311fb 100644
--- a/tools/public_api_guard/cdk/drag-drop.d.ts
+++ b/tools/public_api_guard/cdk/drag-drop.d.ts
@@ -42,7 +42,7 @@ export declare class CdkDrag<T = any> implements AfterViewInit, OnChanges, OnDes
     constructor(
     element: ElementRef<HTMLElement>,
     dropContainer: CdkDropList,
-    _document: any, _ngZone: NgZone, _viewContainerRef: ViewContainerRef, config: DragDropConfig, _dir: Directionality, dragDrop: DragDrop, _changeDetectorRef: ChangeDetectorRef, _selfHandle?: CdkDragHandle | undefined);
+    _document: any, _ngZone: NgZone, _viewContainerRef: ViewContainerRef, config: DragDropConfig, _dir: Directionality, dragDrop: DragDrop, _changeDetectorRef: ChangeDetectorRef, _selfHandle?: CdkDragHandle | undefined, parentDrag?: CdkDrag);
     getFreeDragPosition(): {
         readonly x: number;
         readonly y: number;
@@ -55,7 +55,7 @@ export declare class CdkDrag<T = any> implements AfterViewInit, OnChanges, OnDes
     reset(): void;
     static ngAcceptInputType_disabled: BooleanInput;
     static ɵdir: i0.ɵɵDirectiveDefWithMeta<CdkDrag<any>, "[cdkDrag]", ["cdkDrag"], { "data": "cdkDragData"; "lockAxis": "cdkDragLockAxis"; "rootElementSelector": "cdkDragRootElement"; "boundaryElement": "cdkDragBoundary"; "dragStartDelay": "cdkDragStartDelay"; "freeDragPosition": "cdkDragFreeDragPosition"; "disabled": "cdkDragDisabled"; "constrainPosition": "cdkDragConstrainPosition"; "previewClass": "cdkDragPreviewClass"; }, { "started": "cdkDragStarted"; "released": "cdkDragReleased"; "ended": "cdkDragEnded"; "entered": "cdkDragEntered"; "exited": "cdkDragExited"; "dropped": "cdkDragDropped"; "moved": "cdkDragMoved"; }, ["_previewTemplate", "_placeholderTemplate", "_handles"]>;
-    static ɵfac: i0.ɵɵFactoryDef<CdkDrag<any>, [null, { optional: true; skipSelf: true; }, null, null, null, { optional: true; }, { optional: true; }, null, null, { optional: true; self: true; }]>;
+    static ɵfac: i0.ɵɵFactoryDef<CdkDrag<any>, [null, { optional: true; skipSelf: true; }, null, null, null, { optional: true; }, { optional: true; }, null, null, { optional: true; self: true; }, { optional: true; skipSelf: true; }]>;
 }
 
 export interface CdkDragDrop<T, O = T> {
@@ -321,6 +321,7 @@ export declare class DragRef<T = any> {
 
 export interface DragRefConfig {
     dragStartThreshold: number;
+    parentDragRef?: DragRef;
     pointerDirectionChangeThreshold: number;
     zIndex?: number;
 }