diff --git a/testing/web-platform/tests/web-animations/interfaces/DocumentTimeline/constructor.html b/testing/web-platform/tests/web-animations/interfaces/DocumentTimeline/constructor.html
index e4714be02f8e..ca0997ac8f90 100644
--- a/testing/web-platform/tests/web-animations/interfaces/DocumentTimeline/constructor.html
+++ b/testing/web-platform/tests/web-animations/interfaces/DocumentTimeline/constructor.html
@@ -5,6 +5,7 @@
 <script src="/resources/testharness.js"></script>
 <script src="/resources/testharnessreport.js"></script>
 <script src="../../testcommon.js"></script>
+<script src="../../resources/timing-override.js"></script>
 <body>
 <div id="log"></div>
 <script>
diff --git a/testing/web-platform/tests/web-animations/resources/timing-override.js b/testing/web-platform/tests/web-animations/resources/timing-override.js
new file mode 100755
index 000000000000..a1d65030f02b
--- /dev/null
+++ b/testing/web-platform/tests/web-animations/resources/timing-override.js
@@ -0,0 +1,18 @@
+// Firefox implements unconditional clamping of 20 usec; and for certain web-animation tests,
+// we hit some test failures because the Time Precision is too small. We override these functions
+// on a per-test basis for Firefox only.
+if(navigator.userAgent.toLowerCase().indexOf('firefox') > -1){
+  window.assert_times_equal = (actual, expected, description) => {
+    let TIME_PRECISION = 0.02;
+    assert_approx_equals(actual, expected, TIME_PRECISION * 2, description);
+  };
+
+  window.assert_time_equals_literal = (actual, expected, description) => {
+    let TIME_PRECISION = 0.02;
+    if (Math.abs(expected) === Infinity) {
+      assert_equals(actual, expected, description);
+    } else {
+      assert_approx_equals(actual, expected, TIME_PRECISION, description);
+    }
+  }
+}
diff --git a/testing/web-platform/tests/web-animations/timing-model/animations/finishing-an-animation.html b/testing/web-platform/tests/web-animations/timing-model/animations/finishing-an-animation.html
index cb824ae30ed1..779bee184b8d 100644
--- a/testing/web-platform/tests/web-animations/timing-model/animations/finishing-an-animation.html
+++ b/testing/web-platform/tests/web-animations/timing-model/animations/finishing-an-animation.html
@@ -6,6 +6,7 @@
 <script src="/resources/testharness.js"></script>
 <script src="/resources/testharnessreport.js"></script>
 <script src="../../testcommon.js"></script>
+<script src="../../resources/timing-override.js"></script>
 <body>
 <div id="log"></div>
 <script>
diff --git a/testing/web-platform/tests/web-animations/timing-model/animations/setting-the-start-time-of-an-animation.html b/testing/web-platform/tests/web-animations/timing-model/animations/setting-the-start-time-of-an-animation.html
index 454a294239aa..a1727994bdb9 100644
--- a/testing/web-platform/tests/web-animations/timing-model/animations/setting-the-start-time-of-an-animation.html
+++ b/testing/web-platform/tests/web-animations/timing-model/animations/setting-the-start-time-of-an-animation.html
@@ -5,6 +5,7 @@
 <script src="/resources/testharness.js"></script>
 <script src="/resources/testharnessreport.js"></script>
 <script src="../../testcommon.js"></script>
+<script src="../../resources/timing-override.js"></script>
 <body>
 <div id="log"></div>
 <script>
@@ -262,7 +263,7 @@ promise_test(async t => {
   // calculated using the new playback rate
   assert_times_equal(anim.startTime,
                      anim.timeline.currentTime - 25 * MS_PER_SEC);
-  assert_time_equals_literal(anim.currentTime, 50 * MS_PER_SEC);
+  assert_time_equals_literal(parseInt(anim.currentTime.toPrecision(5), 10), 50 * MS_PER_SEC);
 }, 'Setting the start time of a playing animation applies a pending playback rate');
 
 </script>
diff --git a/testing/web-platform/tests/web-animations/timing-model/animations/the-current-time-of-an-animation.html b/testing/web-platform/tests/web-animations/timing-model/animations/the-current-time-of-an-animation.html
index a0e1a111fd43..77a6b716d220 100644
--- a/testing/web-platform/tests/web-animations/timing-model/animations/the-current-time-of-an-animation.html
+++ b/testing/web-platform/tests/web-animations/timing-model/animations/the-current-time-of-an-animation.html
@@ -5,6 +5,7 @@
 <script src="/resources/testharness.js"></script>
 <script src="/resources/testharnessreport.js"></script>
 <script src="../../testcommon.js"></script>
+<script src="../../resources/timing-override.js"></script>
 <body>
 <div id="log"></div>
 <script>
