diff --git a/reactor-netty-http/src/main/java/reactor/netty/http/client/HttpClientConfig.java b/reactor-netty-http/src/main/java/reactor/netty/http/client/HttpClientConfig.java
index 6003d5f3b0..3a5968f681 100644
--- a/reactor-netty-http/src/main/java/reactor/netty/http/client/HttpClientConfig.java
+++ b/reactor-netty-http/src/main/java/reactor/netty/http/client/HttpClientConfig.java
@@ -574,8 +574,20 @@ static void addStreamHandlers(
 		}
 
 		if (responseTimeoutMillis > -1) {
-			Connection.from(ch).addHandlerFirst(NettyPipeline.ResponseTimeoutHandler,
-					new ReadTimeoutHandler(responseTimeoutMillis, TimeUnit.MILLISECONDS));
+			Connection conn = Connection.from(ch);
+			if (ch.pipeline().get(NettyPipeline.HttpMetricsHandler) != null) {
+				if (ch.pipeline().get(NettyPipeline.ResponseTimeoutHandler) == null) {
+					ch.pipeline().addBefore(NettyPipeline.HttpMetricsHandler, NettyPipeline.ResponseTimeoutHandler,
+							new ReadTimeoutHandler(responseTimeoutMillis, TimeUnit.MILLISECONDS));
+					if (conn.isPersistent()) {
+						conn.onTerminate().subscribe(null, null, () -> conn.removeHandler(NettyPipeline.ResponseTimeoutHandler));
+					}
+				}
+			}
+			else {
+				conn.addHandlerFirst(NettyPipeline.ResponseTimeoutHandler,
+						new ReadTimeoutHandler(responseTimeoutMillis, TimeUnit.MILLISECONDS));
+			}
 		}
 
 		if (log.isDebugEnabled()) {
diff --git a/reactor-netty-http/src/main/java/reactor/netty/http/client/HttpClientOperations.java b/reactor-netty-http/src/main/java/reactor/netty/http/client/HttpClientOperations.java
index dc98049c22..51a14ff49e 100644
--- a/reactor-netty-http/src/main/java/reactor/netty/http/client/HttpClientOperations.java
+++ b/reactor-netty-http/src/main/java/reactor/netty/http/client/HttpClientOperations.java
@@ -639,8 +639,19 @@ else if (markSentBody()) {
 		}
 		listener().onStateChange(this, HttpClientState.REQUEST_SENT);
 		if (responseTimeout != null) {
-			addHandlerFirst(NettyPipeline.ResponseTimeoutHandler,
-					new ReadTimeoutHandler(responseTimeout.toMillis(), TimeUnit.MILLISECONDS));
+			if (channel().pipeline().get(NettyPipeline.HttpMetricsHandler) != null) {
+				if (channel().pipeline().get(NettyPipeline.ResponseTimeoutHandler) == null) {
+					channel().pipeline().addBefore(NettyPipeline.HttpMetricsHandler, NettyPipeline.ResponseTimeoutHandler,
+							new ReadTimeoutHandler(responseTimeout.toMillis(), TimeUnit.MILLISECONDS));
+					if (isPersistent()) {
+						onTerminate().subscribe(null, null, () -> removeHandler(NettyPipeline.ResponseTimeoutHandler));
+					}
+				}
+			}
+			else {
+				addHandlerFirst(NettyPipeline.ResponseTimeoutHandler,
+						new ReadTimeoutHandler(responseTimeout.toMillis(), TimeUnit.MILLISECONDS));
+			}
 		}
 		channel().read();
 		if (channel().parent() != null) {
diff --git a/reactor-netty-http/src/test/java/reactor/netty/http/HttpMetricsHandlerTests.java b/reactor-netty-http/src/test/java/reactor/netty/http/HttpMetricsHandlerTests.java
index c16beb01f4..36108b808f 100644
--- a/reactor-netty-http/src/test/java/reactor/netty/http/HttpMetricsHandlerTests.java
+++ b/reactor-netty-http/src/test/java/reactor/netty/http/HttpMetricsHandlerTests.java
@@ -23,6 +23,7 @@
 import io.netty.channel.ChannelDuplexHandler;
 import io.netty.channel.ChannelHandlerContext;
 import io.netty.channel.ChannelInboundHandlerAdapter;
+import io.netty.channel.ChannelOption;
 import io.netty.channel.ChannelOutboundHandlerAdapter;
 import io.netty.channel.ChannelPipeline;
 import io.netty.channel.ChannelPromise;
@@ -98,6 +99,7 @@
 import static reactor.netty.Metrics.DATA_RECEIVED_TIME;
 import static reactor.netty.Metrics.DATA_SENT;
 import static reactor.netty.Metrics.DATA_SENT_TIME;
+import static reactor.netty.Metrics.ERROR;
 import static reactor.netty.Metrics.ERRORS;
 import static reactor.netty.Metrics.HTTP_CLIENT_PREFIX;
 import static reactor.netty.Metrics.HTTP_SERVER_PREFIX;
@@ -730,12 +732,16 @@ void testServerConnectionsMicrometerConnectionClose(HttpProtocol[] serverProtoco
 			assertThat(ServerCloseHandler.INSTANCE.awaitClientClosedOnServer()).as("awaitClientClosedOnServer timeout").isTrue();
 			assertGauge(registry, SERVER_CONNECTIONS_TOTAL, URI, HTTP, LOCAL_ADDRESS, address).hasValueEqualTo(0);
 			assertGauge(registry, SERVER_CONNECTIONS_ACTIVE, URI, HTTP, LOCAL_ADDRESS, address).hasValueEqualTo(0);
+			// https://github.com/reactor/reactor-netty/issues/3060
+			assertCounter(registry, CLIENT_ERRORS, REMOTE_ADDRESS, address, URI, "/6").hasCountGreaterThanOrEqualTo(1);
 		}
 		else {
 			// make sure the client stream is closed on the server side before checking server metrics
 			assertThat(StreamCloseHandler.INSTANCE.awaitClientClosedOnServer()).as("awaitClientClosedOnServer timeout").isTrue();
 			assertGauge(registry, SERVER_CONNECTIONS_TOTAL, URI, HTTP, LOCAL_ADDRESS, address).hasValueEqualTo(1);
 			assertGauge(registry, SERVER_STREAMS_ACTIVE, URI, HTTP, LOCAL_ADDRESS, address).hasValueEqualTo(0);
+			// https://github.com/reactor/reactor-netty/issues/3060
+			assertCounter(registry, CLIENT_ERRORS, REMOTE_ADDRESS, address, URI, "/6").hasCountGreaterThanOrEqualTo(1);
 			// in case of H2, the tearDown method will ensure client socket is closed on the server side
 		}
 	}
@@ -828,6 +834,8 @@ void testServerConnectionsRecorderConnectionClose(HttpProtocol[] serverProtocols
 			assertThat(ServerRecorder.INSTANCE.onActiveConnectionsAmount.get()).isEqualTo(0);
 			assertThat(ServerRecorder.INSTANCE.onActiveConnectionsLocalAddr.get()).isEqualTo(address);
 			assertThat(ServerRecorder.INSTANCE.onInactiveConnectionsLocalAddr.get()).isEqualTo(address);
+			// https://github.com/reactor/reactor-netty/issues/3060
+			assertCounter(registry, CLIENT_ERRORS, REMOTE_ADDRESS, address, URI, "/7").hasCountGreaterThanOrEqualTo(1);
 		}
 		else {
 			assertThat(StreamCloseHandler.INSTANCE.awaitClientClosedOnServer()).as("awaitClientClosedOnServer timeout").isTrue();
@@ -835,6 +843,8 @@ void testServerConnectionsRecorderConnectionClose(HttpProtocol[] serverProtocols
 			assertThat(ServerRecorder.INSTANCE.onActiveConnectionsAmount.get()).isEqualTo(0);
 			assertThat(ServerRecorder.INSTANCE.onActiveConnectionsLocalAddr.get()).isEqualTo(address);
 			assertThat(ServerRecorder.INSTANCE.onInactiveConnectionsLocalAddr.get()).isEqualTo(address);
+			// https://github.com/reactor/reactor-netty/issues/3060
+			assertCounter(registry, CLIENT_ERRORS, REMOTE_ADDRESS, address, URI, "/7").hasCountGreaterThanOrEqualTo(1);
 			// in case of H2, the tearDown method will ensure client socket is closed on the server side
 		}
 	}
@@ -967,6 +977,27 @@ void testIssue2956(boolean isCustomRecorder, boolean isHttp2) throws Exception {
 		}
 	}
 
+	@ParameterizedTest
+	@MethodSource("httpCompatibleProtocols")
+	void testIssue3060ConnectTimeoutException(HttpProtocol[] serverProtocols, HttpProtocol[] clientProtocols,
+			@Nullable ProtocolSslContextSpec serverCtx, @Nullable ProtocolSslContextSpec clientCtx) throws Exception {
+		CountDownLatch latch = new CountDownLatch(1);
+		customizeClientOptions(httpClient, clientCtx, clientProtocols)
+		        .remoteAddress(() -> new InetSocketAddress("1.1.1.1", 11111))
+		        .option(ChannelOption.CONNECT_TIMEOUT_MILLIS, 10)
+		        .doOnChannelInit((o, c, address) -> c.closeFuture().addListener(f -> latch.countDown()))
+		        .post()
+		        .uri("/1")
+		        .send(ByteBufFlux.fromString(Mono.just("hello")))
+		        .responseContent()
+		        .subscribe();
+
+		assertThat(latch.await(30, TimeUnit.SECONDS)).as("latch await").isTrue();
+
+		String[] summaryTags = new String[]{REMOTE_ADDRESS, "1.1.1.1:11111", STATUS, ERROR};
+		assertTimer(registry, CLIENT_CONNECT_TIME, summaryTags).hasCountEqualTo(1);
+	}
+
 	static Stream<Arguments> combinationsIssue2956() {
 		return Stream.of(
 				// isCustomRecorder, isHttp2