diff --git a/DEPS b/DEPS
index 00cb7f7..4180192 100644
--- a/DEPS
+++ b/DEPS
@@ -133,7 +133,7 @@
   "ply_rev": "604b32590ffad5cbb82e4afef1d305512d06ae93",
   "pool_rev": "7abe634002a1ba8a0928eded086062f1307ccfae",
   "protobuf_rev": "0d03fd588df69e9863e2a2efc0059dee8f18d5b2",
-  "pub_rev": "0e657414a472e74ca5dd76ae0db50cc060251dec",
+  "pub_rev": "0db3255b72db2957d50ea4f13c5c23835f42e5c6",
   "pub_semver_rev": "10569a1e867e909cf5db201f73118020453e5db8",
   "resource_rev": "6b79867d0becf5395e5819a75720963b8298e9a7",
   "root_certificates_rev": "7e5ec82c99677a2e5b95ce296c4d68b0d3378ed8",
diff --git a/sdk/lib/_http/http_impl.dart b/sdk/lib/_http/http_impl.dart
index eac06c4..e99a58d 100644
--- a/sdk/lib/_http/http_impl.dart
+++ b/sdk/lib/_http/http_impl.dart
@@ -2219,25 +2219,10 @@
       Future socketFuture = task.socket;
       final Duration? connectionTimeout = client.connectionTimeout;
       if (connectionTimeout != null) {
-        socketFuture = socketFuture.timeout(connectionTimeout, onTimeout: () {
-          _socketTasks.remove(task);
-          task.cancel();
-          return null;
-        });
+        socketFuture = socketFuture.timeout(connectionTimeout);
       }
       return socketFuture.then((socket) {
-        // When there is a timeout, there is a race in which the connectionTask
-        // Future won't be completed with an error before the socketFuture here
-        // is completed with 'null' by the onTimeout callback above. In this
-        // case, propagate a SocketException as specified by the
-        // HttpClient.connectionTimeout docs.
         _connecting--;
-        if (socket == null) {
-          assert(connectionTimeout != null);
-          throw new SocketException(
-              "HTTP connection timed out after ${connectionTimeout}, "
-              "host: ${host}, port: ${port}");
-        }
         socket.setOption(SocketOption.tcpNoDelay, true);
         var connection =
             new _HttpClientConnection(key, socket, client, false, context);
@@ -2258,6 +2243,20 @@
           return new _ConnectionInfo(connection, proxy);
         }
       }, onError: (error) {
+        // When there is a timeout, there is a race in which the connectionTask
+        // Future won't be completed with an error before the socketFuture here
+        // is completed with a TimeoutException by the onTimeout callback above.
+        // In this case, propagate a SocketException as specified by the
+        // HttpClient.connectionTimeout docs.
+        if (error is TimeoutException) {
+          assert(connectionTimeout != null);
+          _connecting--;
+          _socketTasks.remove(task);
+          task.cancel();
+          throw SocketException(
+              "HTTP connection timed out after ${connectionTimeout}, "
+              "host: ${host}, port: ${port}");
+        }
         _socketTasks.remove(task);
         _checkPending();
         throw error;
diff --git a/tests/standalone/io/regress_44895.dart b/tests/standalone/io/regress_44895.dart
new file mode 100644
index 0000000..38c0110a
--- /dev/null
+++ b/tests/standalone/io/regress_44895.dart
@@ -0,0 +1,17 @@
+// Copyright (c) 2021, the Dart project authors.  Please see the AUTHORS file
+// for details. All rights reserved. Use of this source code is governed by a
+// BSD-style license that can be found in the LICENSE file.
+
+import "dart:io";
+
+void main() {
+  final client = HttpClient();
+  client.connectionTimeout = Duration.zero;
+  // Should not throw a type error.
+  client.openUrl(
+    'get',
+    Uri.parse(
+      'https://localhost/',
+    ),
+  );
+}
diff --git a/tools/VERSION b/tools/VERSION
index 856cb76..325a6a0 100644
--- a/tools/VERSION
+++ b/tools/VERSION
@@ -28,4 +28,4 @@
 MINOR 12
 PATCH 0
 PRERELEASE 259
-PRERELEASE_PATCH 12
\ No newline at end of file
+PRERELEASE_PATCH 14
\ No newline at end of file