diff --git a/lib/https.js b/lib/https.js
index 1e86e81cf76b15..1b9df4c88ee882 100644
--- a/lib/https.js
+++ b/lib/https.js
@@ -221,7 +221,6 @@ function establishTunnel(agent, socket, options, tunnelConfig, afterSocket) {
         break;
       }
     }
-    socket.on('readable', read);
   }
 
   function cleanup() {
@@ -315,6 +314,7 @@ function establishTunnel(agent, socket, options, tunnelConfig, afterSocket) {
 
   socket.on('error', onProxyError);
   socket.on('end', onProxyEnd);
+  socket.on('readable', read);
   socket.write(proxyTunnelPayload);
 
   read();
diff --git a/test/client-proxy/test-https-proxy-request-slow-connect-response.mjs b/test/client-proxy/test-https-proxy-request-slow-connect-response.mjs
new file mode 100644
index 00000000000000..d75f49e1516109
--- /dev/null
+++ b/test/client-proxy/test-https-proxy-request-slow-connect-response.mjs
@@ -0,0 +1,97 @@
+// Regression test for https://github.com/nodejs/node/issues/62904.
+// This test drives that scenario by writing the CONNECT response one byte at
+// a time with a short delay between writes, and asserts that no warning is
+// ever emitted while the full HTTPS response is received correctly.
+
+import * as common from '../common/index.mjs';
+import fixtures from '../common/fixtures.js';
+import assert from 'node:assert';
+import http from 'node:http';
+import net from 'node:net';
+import { once } from 'events';
+
+if (!common.hasCrypto)
+  common.skip('missing crypto');
+
+// https must be dynamically imported so that builds without crypto support
+// can skip it.
+const { default: https } = await import('node:https');
+
+// Target HTTPS server the client ultimately wants to reach.
+const server = https.createServer({
+  cert: fixtures.readKey('agent8-cert.pem'),
+  key: fixtures.readKey('agent8-key.pem'),
+}, common.mustCall((req, res) => {
+  res.end('Hello world');
+}));
+server.on('error', common.mustNotCall((err) => { console.error('Server error', err); }));
+server.listen(0);
+await once(server, 'listening');
+
+// Proxy server that writes the CONNECT response one byte at a time. Using the
+// built-in HTTP server avoids having to parse the CONNECT request ourselves
+// (which cannot rely on a single TCP chunk containing the whole request line).
+const proxy = http.createServer();
+proxy.on('connect', common.mustCall(async (req, res, head) => {
+  const { hostname, port } = new URL(`https://${req.url}`);
+  const normalizedHost = hostname.startsWith('[') && hostname.endsWith(']') ?
+    hostname.slice(1, -1) : hostname;
+
+  const upstream = net.connect(Number(port), normalizedHost);
+  upstream.on('error', () => res.destroy());
+  res.on('error', () => upstream.destroy());
+  await once(upstream, 'connect');
+
+  const response = 'HTTP/1.1 200 Connection Established\r\n' +
+                  'Proxy-agent: Node.js-Proxy\r\n' +
+                  '\r\n';
+  // Feed the response byte by byte with a macrotask boundary between writes
+  // so the client sees many separate 'readable' events during tunnel setup.
+  // This is what triggers the listener leak described in the issue.
+  for (let i = 0; i < response.length; i++) {
+    if (res.destroyed) {
+      upstream.destroy();
+      return;
+    }
+    res.write(response[i]);
+    await new Promise((resolve) => setImmediate(resolve));
+  }
+  if (head?.length) upstream.write(head);
+  res.pipe(upstream);
+  upstream.pipe(res);
+}, 1));
+proxy.on('error', common.mustNotCall((err) => { console.error('Proxy error', err); }));
+proxy.listen(0);
+await once(proxy, 'listening');
+
+// No warning should be emitted during the proxied request. The pre-fix code
+// emits MaxListenersExceededWarning; any other warning here would also be
+// unexpected and should fail the test.
+process.on('warning',
+           common.mustNotCall('unexpected warning during proxied request'));
+
+const agent = new https.Agent({
+  proxyEnv: {
+    HTTPS_PROXY: `http://localhost:${proxy.address().port}`,
+  },
+  ca: fixtures.readKey('fake-startcom-root-cert.pem'),
+});
+
+const req = https.request({
+  hostname: 'localhost',
+  port: server.address().port,
+  path: '/test',
+  agent,
+}, common.mustCall((res) => {
+  let data = '';
+  res.setEncoding('utf8');
+  res.on('data', (chunk) => { data += chunk; });
+  res.on('end', common.mustCall(() => {
+    assert.strictEqual(data, 'Hello world');
+    assert.strictEqual(res.statusCode, 200);
+    proxy.close();
+    server.close();
+  }));
+}));
+req.on('error', common.mustNotCall());
+req.end();