diff --git a/lib/_http_client.js b/lib/_http_client.js
index 63a7befc8ebbb3..a80ff906f978ba 100644
--- a/lib/_http_client.js
+++ b/lib/_http_client.js
@@ -115,6 +115,8 @@ let debug = require('internal/util/debuglog').debuglog('http', (fn) => {
 
 const INVALID_PATH_REGEX = /[^\u0021-\u00ff]/;
 const kError = Symbol('kError');
+const kImmediateError = Symbol('kImmediateError');
+const kOnImmediateError = Symbol('kOnImmediateError');
 
 const kLenientAll = HTTPParser.kLenientAll | 0;
 const kLenientNone = HTTPParser.kLenientNone | 0;
@@ -898,6 +900,7 @@ function tickOnSocket(req, socket) {
   parser.joinDuplicateHeaders = req.joinDuplicateHeaders;
 
   parser.onIncoming = parserOnIncomingClient;
+  socket.removeListener('error', socket[kOnImmediateError]);
   socket.on('error', socketErrorListener);
   socket.on('data', socketOnData);
   socket.on('end', socketOnEnd);
@@ -937,27 +940,36 @@ function listenSocketTimeout(req) {
 }
 
 ClientRequest.prototype.onSocket = function onSocket(socket, err) {
-  // TODO(ronag): Between here and onSocketNT the socket
-  // has no 'error' handler.
+  const req = this;
+
+  if (!err && socket) {
+    socket[kOnImmediateError] = function onImmediateError(err) {
+      req[kImmediateError] = err;
+    }
+    socket.on('error', socket[kOnImmediateError]);
+  }
+
   process.nextTick(onSocketNT, this, socket, err);
 };
 
 function onSocketNT(req, socket, err) {
-  if (req.destroyed || err) {
+  if (req.destroyed || err || req[kImmediateError]) {
     req.destroyed = true;
 
     function _destroy(req, err) {
       if (!req.aborted && !err) {
         err = new ConnResetException('socket hang up');
       }
-      if (err) {
-        emitErrorEvent(req, err);
+      if (err || req[kImmediateError] instanceof Error) {
+        const finalError = req[kImmediateError] ? req[kImmediateError] : err;
+        emitErrorEvent(req, finalError);
       }
       req._closed = true;
       req.emit('close');
     }
 
     if (socket) {
+      socket.removeListener('error', socket[kOnImmediateError]);
       if (!err && req.agent && !socket.destroyed) {
         socket.emit('free');
       } else {
diff --git a/test/parallel/test-http-client-immediate-error.js b/test/parallel/test-http-client-immediate-error.js
index ff29ad72bd8585..e00db37a2182ee 100644
--- a/test/parallel/test-http-client-immediate-error.js
+++ b/test/parallel/test-http-client-immediate-error.js
@@ -5,40 +5,116 @@
 // net.createConnection().
 
 const common = require('../common');
+console.log('require completed: common', Date.now());
 const assert = require('assert');
+console.log('require completed: assert', Date.now());
 const net = require('net');
+console.log('require completed: net', Date.now());
 const http = require('http');
+console.log('require completed: http', Date.now());
 const { internalBinding } = require('internal/test/binding');
-const { UV_ENETUNREACH } = internalBinding('uv');
+console.log('require completed: internal/test/binding', Date.now());
+const { UV_ENETUNREACH, UV_EADDRINUSE } = internalBinding('uv');
 const {
   newAsyncId,
   symbols: { async_id_symbol }
 } = require('internal/async_hooks');
+console.log('require completed: internal/async_hooks', Date.now());
 
-const agent = new http.Agent();
-agent.createConnection = common.mustCall((cfg) => {
-  const sock = new net.Socket();
+const config = {
+  host: 'http://example.com',
+  // We need to specify 'family' in both items of the array so 'internalConnectMultiple' is invoked
+  connectMultiple: [{ address: '192.4.4.4', family: 4 }, { address: '200::1', family: 6 }],
+  connectSolo: { address: '192.4.4.4', family: 4 },
+};
 
-  // Fake the handle so we can enforce returning an immediate error
-  sock._handle = {
-    connect: common.mustCall((req, addr, port) => {
-      return UV_ENETUNREACH;
-    }),
-    readStart() {},
-    close() {}
-  };
+function agentFactory(handle, count) {
+  const agent = new http.Agent();
+  agent.createConnection = common.mustCall((...cfg) => {
+    const normalized = net._normalizeArgs(cfg);
+    const sock = new net.Socket();
 
-  // Simulate just enough socket handle initialization
-  sock[async_id_symbol] = newAsyncId();
+    // Fake the handle so we can enforce returning an immediate error
+    sock._handle = handle;
 
-  sock.connect(cfg);
-  return sock;
+    // Simulate just enough socket handle initialization
+    sock[async_id_symbol] = newAsyncId();
+
+    sock.connect(normalized);
+    return sock;
+  }, count);
+
+  return agent;
+};
+
+const handleWithoutBind = (callCount) => ({
+  connect: common.mustCall((req, addr, port) => {
+    return UV_ENETUNREACH;
+  }, callCount),
+  readStart() { },
+  close() { },
+});
+
+const handleWithBind = (callCount) => ({
+  readStart() { },
+  close() { },
+  bind: common.mustCall(() => UV_EADDRINUSE, callCount),
 });
 
+const agentWithoutBind = agentFactory(handleWithoutBind(3), 3); // Because three tests will use this
+const agentWithBind = agentFactory(handleWithBind(2), 2); // Because two tests will use this handle
+
+console.log('test initiated: test-1', Date.now());
 http.get({
   host: '127.0.0.1',
   port: 1,
-  agent
+  agent: agentWithoutBind,
+}).on('error', common.mustCall((err) => {
+  assert.strictEqual(err.code, 'ENETUNREACH');
+  console.log('test completed: test-1', Date.now());
+}));
+
+console.log('test initiated: test-2', Date.now());
+http.request(config.host, {
+  agent: agentWithoutBind,
+  lookup(_0, _1, cb) {
+    cb(null, config.connectMultiple);
+  },
 }).on('error', common.mustCall((err) => {
   assert.strictEqual(err.code, 'ENETUNREACH');
+  console.log('test completed: test-2', Date.now());
+}));
+
+console.log('test initiated: test-3', Date.now());
+http.request(config.host, {
+  agent: agentWithoutBind,
+  lookup(_0, _1, cb) {
+    cb(null, config.connectSolo.address, config.connectSolo.family);
+  },
+  family: 4,
+}).on('error', common.mustCall((err) => {
+  assert.strictEqual(err.code, 'ENETUNREACH');
+  console.log('test completed: test-3', Date.now());
+}));
+
+console.log('test initiated: test-4', Date.now());
+http.request(config.host, {
+  agent: agentWithBind,
+  family: 4, // We specify 'family' so 'internalConnect' is invoked
+  localPort: 2222 // Required to trigger _handle.bind()
+}).on('error', common.mustCall((err) => {
+  assert.strictEqual(err.code, 'EADDRINUSE');
+  console.log('test completed: test-4', Date.now());
+}));
+
+console.log('test initiated: test-5', Date.now());
+http.request(config.host, {
+  agent: agentWithBind,
+  lookup(_0, _1, cb) {
+    cb(null, config.connectMultiple);
+  },
+  localPort: 2222, // Required to trigger _handle.bind()
+}).on('error', common.mustCall((err) => {
+  assert.strictEqual(err.code, 'EADDRINUSE');
+  console.log('test completed: test-5', Date.now());
 }));