diff --git a/akka-http-core/src/main/scala/akka/http/impl/engine/client/OutgoingConnectionBlueprint.scala b/akka-http-core/src/main/scala/akka/http/impl/engine/client/OutgoingConnectionBlueprint.scala
index 91a02beb81..b1fb9040e9 100644
--- a/akka-http-core/src/main/scala/akka/http/impl/engine/client/OutgoingConnectionBlueprint.scala
+++ b/akka-http-core/src/main/scala/akka/http/impl/engine/client/OutgoingConnectionBlueprint.scala
@@ -78,7 +78,7 @@ private[http] object OutgoingConnectionBlueprint {
       val terminationFanout = b.add(Broadcast[HttpResponse](2))
       val terminationMerge = b.add(TerminationMerge)
 
-      val logger = b.add(ErrorHandling[ByteString]((t: Throwable) ⇒ log.error(t, "Outgoing request stream error")).named("errorLogger"))
+      val logger = b.add(MapError[ByteString] { case t ⇒ log.error(t, "Outgoing request stream error"); t }.named("errorLogger"))
       val wrapTls = b.add(Flow[ByteString].map(SendBytes))
       terminationMerge.out ~> requestRendering ~> logger ~> wrapTls
 
diff --git a/akka-http-core/src/main/scala/akka/http/impl/engine/server/HttpServerBluePrint.scala b/akka-http-core/src/main/scala/akka/http/impl/engine/server/HttpServerBluePrint.scala
index caff5e35ca..7f0a5c83d1 100644
--- a/akka-http-core/src/main/scala/akka/http/impl/engine/server/HttpServerBluePrint.scala
+++ b/akka-http-core/src/main/scala/akka/http/impl/engine/server/HttpServerBluePrint.scala
@@ -240,15 +240,15 @@ private[http] object HttpServerBluePrint {
 
     val responseRendererFactory = new HttpResponseRendererFactory(serverHeader, responseHeaderSizeHint, log)
 
-    val errorHandler: Throwable ⇒ Unit = {
+    val errorHandler: PartialFunction[Throwable, Throwable] = {
       // idle timeouts should not result in errors in the log. See 19058.
-      case timeout: HttpConnectionTimeoutException ⇒ log.debug(s"Closing HttpConnection due to timeout: ${timeout.getMessage}")
-      case t                                       ⇒ log.error(t, "Outgoing response stream error")
+      case timeout: HttpConnectionTimeoutException ⇒ log.debug(s"Closing HttpConnection due to timeout: ${timeout.getMessage}"); timeout
+      case t                                       ⇒ log.error(t, "Outgoing response stream error"); t
     }
 
     Flow[ResponseRenderingContext]
       .via(responseRendererFactory.renderer.named("renderer"))
-      .via(ErrorHandling[ResponseRenderingOutput](errorHandler).named("errorLogger"))
+      .via(MapError[ResponseRenderingOutput](errorHandler).named("errorLogger"))
   }
 
   class RequestTimeoutSupport(initialTimeout: FiniteDuration)
diff --git a/akka-http-core/src/main/scala/akka/http/impl/util/package.scala b/akka-http-core/src/main/scala/akka/http/impl/util/package.scala
index 76f108d695..f213ebd17b 100644
--- a/akka-http-core/src/main/scala/akka/http/impl/util/package.scala
+++ b/akka-http-core/src/main/scala/akka/http/impl/util/package.scala
@@ -106,15 +106,17 @@ package util {
   import akka.stream.{ Attributes, Outlet, Inlet, FlowShape }
   import scala.concurrent.duration.FiniteDuration
 
-  private[http] final case class ErrorHandling[T](handler: Throwable ⇒ Unit) extends SimpleLinearGraphStage[T] {
+  /**
+   * Maps error with the provided function if it is defined for an error or, otherwise, passes it on unchanged.
+   */
+  private[http] final case class MapError[T](f: PartialFunction[Throwable, Throwable]) extends SimpleLinearGraphStage[T] {
     override def createLogic(attr: Attributes) =
       new GraphStageLogic(shape) with InHandler with OutHandler {
         override def onPush(): Unit = push(out, grab(in))
 
-        override def onUpstreamFailure(ex: Throwable): Unit = {
-          handler(ex)
-          super.onUpstreamFailure(ex)
-        }
+        override def onUpstreamFailure(ex: Throwable): Unit =
+          if (f.isDefinedAt(ex)) super.onUpstreamFailure(f(ex))
+          else super.onUpstreamFailure(ex)
 
         override def onPull(): Unit = pull(in)
 
diff --git a/akka-http-core/src/main/scala/akka/http/scaladsl/Http.scala b/akka-http-core/src/main/scala/akka/http/scaladsl/Http.scala
index 4e71874794..fbc2a13f5d 100644
--- a/akka-http-core/src/main/scala/akka/http/scaladsl/Http.scala
+++ b/akka-http-core/src/main/scala/akka/http/scaladsl/Http.scala
@@ -15,7 +15,7 @@ import akka.http.impl.engine.client._
 import akka.http.impl.engine.server._
 import akka.http.impl.engine.ws.WebSocketClientBlueprint
 import akka.http.impl.settings.{ ConnectionPoolSetup, HostConnectionPoolSetup }
-import akka.http.impl.util.StreamUtils
+import akka.http.impl.util.{ MapError, StreamUtils }
 import akka.http.scaladsl.model._
 import akka.http.scaladsl.model.headers.Host
 import akka.http.scaladsl.model.ws.{ Message, WebSocketRequest, WebSocketUpgradeResponse }
@@ -85,7 +85,7 @@ class HttpExt(private val config: Config)(implicit val system: ActorSystem) exte
     connections.map {
       case Tcp.IncomingConnection(localAddress, remoteAddress, flow) ⇒
         val layer = serverLayer(settings, Some(remoteAddress), log)
-        val flowWithTimeoutRecovered = flow.recover { case t: TimeoutException ⇒ throw new HttpConnectionTimeoutException(t.getMessage) }
+        val flowWithTimeoutRecovered = flow.via(MapError { case t: TimeoutException ⇒ new HttpConnectionTimeoutException(t.getMessage) })
         IncomingConnection(localAddress, remoteAddress, layer atop tlsStage join flowWithTimeoutRecovered)
     }.mapMaterializedValue {
       _.map(tcpBinding ⇒ ServerBinding(tcpBinding.localAddress)(() ⇒ tcpBinding.unbind()))(fm.executionContext)