diff --git a/CHANGELOG.md b/CHANGELOG.md
index 47daaf340e1a..94c07afdff0d 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -61,6 +61,8 @@
 
 ### Fixes
 
+* `[jest-mock]` [**BREAKING**] Replace timestamps with `invocationCallOrder`
+  ([#5867](https://github.com/facebook/jest/pull/5867))
 * `[jest-jasmine2]` Install `sourcemap-support` into normal runtime to catch
   runtime errors ([#5945](https://github.com/facebook/jest/pull/5945))
 * `[jest-jasmine2]` Added assertion error handling inside `afterAll hook`
diff --git a/packages/jest-mock/README.md b/packages/jest-mock/README.md
index 0ab9815944a4..41d983e379d8 100644
--- a/packages/jest-mock/README.md
+++ b/packages/jest-mock/README.md
@@ -78,12 +78,12 @@ following members:
 
 ##### `.mock`
 
-An object with three members, `calls`, `instances` and `timestamps`, which are
-all lists. The items in the `calls` list are the arguments with which the
-function was called. The "instances" list stores the value of 'this' for each
-call to the function. This is useful for retrieving instances from a
-constructor. The `timestamps` list stores a number timestamp every time the mock
-is called.
+An object with three members, `calls`, `instances` and `invocationCallOrder`,
+which are all lists. The items in the `calls` list are the arguments with which
+the function was called. The "instances" list stores the value of 'this' for
+each call to the function. This is useful for retrieving instances from a
+constructor. The `invocationCallOrder` lists the order in which the mock was
+called in relation to all mock calls, starting at 1.
 
 ##### `.mockReturnValueOnce(value)`
 
diff --git a/packages/jest-mock/src/__tests__/jest_mock.test.js b/packages/jest-mock/src/__tests__/jest_mock.test.js
index 7c3f983aa027..6c2437f4b43a 100644
--- a/packages/jest-mock/src/__tests__/jest_mock.test.js
+++ b/packages/jest-mock/src/__tests__/jest_mock.test.js
@@ -508,67 +508,64 @@ describe('moduleMocker', () => {
       expect(fn.mock.thrownErrors).toEqual([undefined, error, undefined]);
     });
 
-    describe('timestamps', () => {
-      const RealDate = Date;
-
-      beforeEach(() => {
-        global.Date = {
-          now: jest
-            .fn()
-            .mockImplementationOnce(() => 978391040765)
-            .mockImplementationOnce(() => 1262388620765),
-        };
-      });
+    describe('invocationCallOrder', () => {
+      it('tracks invocationCallOrder made by mocks', () => {
+        const fn1 = moduleMocker.fn();
+        expect(fn1.mock.invocationCallOrder).toEqual([]);
 
-      afterEach(() => {
-        global.Date = RealDate;
-      });
+        fn1(1, 2, 3);
+        expect(fn1.mock.invocationCallOrder[0]).toBe(1);
 
-      it('tracks timestamps made by mocks', () => {
-        const fn = moduleMocker.fn();
-        expect(fn.mock.timestamps).toEqual([]);
+        fn1('a', 'b', 'c');
+        expect(fn1.mock.invocationCallOrder[1]).toBe(2);
 
-        fn(1, 2, 3);
-        expect(fn.mock.timestamps[0]).toBe(978391040765);
+        fn1(1, 2, 3);
+        expect(fn1.mock.invocationCallOrder[2]).toBe(3);
 
-        fn('a', 'b', 'c');
-        expect(fn.mock.timestamps[1]).toBe(1262388620765);
+        const fn2 = moduleMocker.fn();
+        expect(fn2.mock.invocationCallOrder).toEqual([]);
+
+        fn2('d', 'e', 'f');
+        expect(fn2.mock.invocationCallOrder[0]).toBe(4);
+
+        fn2(4, 5, 6);
+        expect(fn2.mock.invocationCallOrder[1]).toBe(5);
       });
 
-      it('supports clearing mock timestamps', () => {
+      it('supports clearing mock invocationCallOrder', () => {
         const fn = moduleMocker.fn();
-        expect(fn.mock.timestamps).toEqual([]);
+        expect(fn.mock.invocationCallOrder).toEqual([]);
 
         fn(1, 2, 3);
-        expect(fn.mock.timestamps).toEqual([978391040765]);
+        expect(fn.mock.invocationCallOrder).toEqual([1]);
 
         fn.mockReturnValue('abcd');
 
         fn.mockClear();
-        expect(fn.mock.timestamps).toEqual([]);
+        expect(fn.mock.invocationCallOrder).toEqual([]);
 
         fn('a', 'b', 'c');
-        expect(fn.mock.timestamps).toEqual([1262388620765]);
+        expect(fn.mock.invocationCallOrder).toEqual([2]);
 
         expect(fn()).toEqual('abcd');
       });
 
-      it('supports clearing all mocks timestamps', () => {
+      it('supports clearing all mocks invocationCallOrder', () => {
         const fn1 = moduleMocker.fn();
         fn1.mockImplementation(() => 'abcd');
 
         fn1(1, 2, 3);
-        expect(fn1.mock.timestamps).toEqual([978391040765]);
+        expect(fn1.mock.invocationCallOrder).toEqual([1]);
 
         const fn2 = moduleMocker.fn();
 
         fn2.mockReturnValue('abcde');
         fn2('a', 'b', 'c', 'd');
-        expect(fn2.mock.timestamps).toEqual([1262388620765]);
+        expect(fn2.mock.invocationCallOrder).toEqual([2]);
 
         moduleMocker.clearAllMocks();
-        expect(fn1.mock.timestamps).toEqual([]);
-        expect(fn2.mock.timestamps).toEqual([]);
+        expect(fn1.mock.invocationCallOrder).toEqual([]);
+        expect(fn2.mock.invocationCallOrder).toEqual([]);
         expect(fn1()).toEqual('abcd');
         expect(fn2()).toEqual('abcde');
       });
diff --git a/packages/jest-mock/src/index.js b/packages/jest-mock/src/index.js
index 0f5dc8c91e2c..f99aad8c144e 100644
--- a/packages/jest-mock/src/index.js
+++ b/packages/jest-mock/src/index.js
@@ -26,7 +26,7 @@ type MockFunctionState = {
   calls: Array<Array<any>>,
   returnValues: Array<any>,
   thrownErrors: Array<any>,
-  timestamps: Array<number>,
+  invocationCallOrder: Array<number>,
 };
 
 type MockFunctionConfig = {
@@ -241,6 +241,7 @@ class ModuleMockerClass {
   _mockConfigRegistry: WeakMap<Function, MockFunctionConfig>;
   _spyState: Set<() => void>;
   ModuleMocker: Class<ModuleMockerClass>;
+  _invocationCallCounter: number;
 
   /**
    * @see README.md
@@ -253,6 +254,7 @@ class ModuleMockerClass {
     this._mockConfigRegistry = new WeakMap();
     this._spyState = new Set();
     this.ModuleMocker = ModuleMockerClass;
+    this._invocationCallCounter = 1;
   }
 
   _ensureMockConfig(f: Mock): MockFunctionConfig {
@@ -288,9 +290,9 @@ class ModuleMockerClass {
     return {
       calls: [],
       instances: [],
+      invocationCallOrder: [],
       returnValues: [],
       thrownErrors: [],
-      timestamps: [],
     };
   }
 
@@ -325,7 +327,7 @@ class ModuleMockerClass {
         const mockConfig = mocker._ensureMockConfig(f);
         mockState.instances.push(this);
         mockState.calls.push(Array.prototype.slice.call(arguments));
-        mockState.timestamps.push(Date.now());
+        mockState.invocationCallOrder.push(mocker._invocationCallCounter++);
 
         // Will be set to the return value of the mock if an error is not thrown
         let finalReturnValue;