diff --git a/src/v3/apiWatch.ts b/src/v3/apiWatch.ts
index 141a58eb686..7160009dabb 100644
--- a/src/v3/apiWatch.ts
+++ b/src/v3/apiWatch.ts
@@ -185,8 +185,11 @@ function doWatch(
   }
 
   const instance = currentInstance
-  const call = (fn: Function, type: string, args: any[] | null = null) =>
-    invokeWithErrorHandling(fn, null, args, instance, type)
+  const call = (fn: Function, type: string, args: any[] | null = null) => {
+    const res = invokeWithErrorHandling(fn, null, args, instance, type)
+    if (deep && res && res.__ob__) res.__ob__.dep.depend()
+    return res
+  }
 
   let getter: () => any
   let forceTrigger = false
@@ -209,6 +212,7 @@ function doWatch(
         if (isRef(s)) {
           return s.value
         } else if (isReactive(s)) {
+          s.__ob__.dep.depend()
           return traverse(s)
         } else if (isFunction(s)) {
           return call(s, WATCHER_GETTER)
diff --git a/test/unit/features/v3/apiWatch.spec.ts b/test/unit/features/v3/apiWatch.spec.ts
index c92bc150ae7..a684d16116e 100644
--- a/test/unit/features/v3/apiWatch.spec.ts
+++ b/test/unit/features/v3/apiWatch.spec.ts
@@ -1200,4 +1200,35 @@ describe('api: watch', () => {
     expect(parentSpy).toHaveBeenCalledTimes(1)
     expect(childSpy).toHaveBeenCalledTimes(1)
   })
+
+  // #12967
+  test('trigger when adding new property with Vue.set (getter)', async () => {
+    const spy = vi.fn()
+    const r = reactive({ exist: 5 })
+    watch(() => r, spy, { deep: true })
+    set(r, 'add', 1)
+
+    await nextTick()
+    expect(spy).toHaveBeenCalledTimes(1)
+  })
+
+  test('trigger when adding new property with Vue.set (getter in array source)', async () => {
+    const spy = vi.fn()
+    const r = reactive({ exist: 5 })
+    watch([() => r], spy, { deep: true })
+    set(r, 'add', 1)
+
+    await nextTick()
+    expect(spy).toHaveBeenCalledTimes(1)
+  })
+
+  test('trigger when adding new property with Vue.set (reactive in array source)', async () => {
+    const spy = vi.fn()
+    const r = reactive({ exist: 5 })
+    watch([r], spy, { deep: true })
+    set(r, 'add', 1)
+
+    await nextTick()
+    expect(spy).toHaveBeenCalledTimes(1)
+  })
 })