diff --git a/src/Servers/Kestrel/shared/test/MockSystemClock.cs b/src/Servers/Kestrel/shared/test/MockSystemClock.cs
index 5ec904aad0..61a3d6e123 100644
--- a/src/Servers/Kestrel/shared/test/MockSystemClock.cs
+++ b/src/Servers/Kestrel/shared/test/MockSystemClock.cs
@@ -9,7 +9,16 @@ namespace Microsoft.AspNetCore.Testing
 {
     public class MockSystemClock : ISystemClock
     {
-        private long _utcNowTicks = DateTimeOffset.UtcNow.Ticks;
+        private static Random _random = new Random();
+
+        private long _utcNowTicks;
+
+        public MockSystemClock()
+        {
+            // Use a random DateTimeOffset to ensure tests that incorrectly use the current DateTimeOffset fail always instead of only rarely.
+            // Pick a date between the min DateTimeOffset and a day before the max DateTimeOffset so there's room to advance the clock.
+            _utcNowTicks = NextLong(DateTimeOffset.MinValue.Ticks, DateTimeOffset.MaxValue.Ticks - TimeSpan.FromDays(1).Ticks);
+        }
 
         public DateTimeOffset UtcNow
         {
@@ -29,5 +38,10 @@ namespace Microsoft.AspNetCore.Testing
         public DateTimeOffset UtcNowUnsynchronized => UtcNow;
 
         public int UtcNowCalled { get; private set; }
+
+        private long NextLong(long minValue, long maxValue)
+        {
+            return (long)(_random.NextDouble() * (maxValue - minValue) + minValue);
+        }
     }
 }
diff --git a/src/Servers/Kestrel/test/InMemory.FunctionalTests/RequestTests.cs b/src/Servers/Kestrel/test/InMemory.FunctionalTests/RequestTests.cs
index a89f552696..b2be3c2db8 100644
--- a/src/Servers/Kestrel/test/InMemory.FunctionalTests/RequestTests.cs
+++ b/src/Servers/Kestrel/test/InMemory.FunctionalTests/RequestTests.cs
@@ -130,7 +130,6 @@ namespace Microsoft.AspNetCore.Server.Kestrel.InMemory.FunctionalTests
         [Fact]
         public async Task CanUpgradeRequestWithConnectionKeepAliveUpgradeHeader()
         {
-            var testContext = new TestServiceContext();
             var dataRead = false;
 
             using (var server = new TestServer(async context =>
@@ -154,7 +153,7 @@ namespace Microsoft.AspNetCore.Server.Kestrel.InMemory.FunctionalTests
                     await connection.ReceiveEnd(
                         "HTTP/1.1 101 Switching Protocols",
                         "Connection: Upgrade",
-                        $"Date: {testContext.DateHeaderValue}",
+                        $"Date: {server.Context.DateHeaderValue}",
                         "",
                         "");
                 }