diff --git a/lib/_http_client.js b/lib/_http_client.js
index adcacb752e6..4687f927e9d 100644
--- a/lib/_http_client.js
+++ b/lib/_http_client.js
@@ -880,6 +880,13 @@ function statusIsInformational(status) {
   return (status < 200 && status >= 100 && status !== 101);
 }
 
+function responseCannotContainMessageBody(status, method) {
+  // RFC9112 Section 6.1.1
+  return method === 'HEAD' ||
+    status === 204 ||
+    status === 304;
+}
+
 // client
 function parserOnIncomingClient(res, shouldKeepAlive) {
   const socket = this.socket;
@@ -934,11 +941,18 @@ function parserOnIncomingClient(res, shouldKeepAlive) {
     return 1;  // Skip body but don't treat as Upgrade.
   }
 
-  if (req.shouldKeepAlive && !shouldKeepAlive && !req.upgradeOrConnect) {
+  if (req.shouldKeepAlive && !req.upgradeOrConnect) {
+    // Socket may be kept alive and response cannot contain
+    // a message body, resume to allow socket to return to free pool
+    if (responseCannotContainMessageBody(res.statusCode, method)) {
+      res.resume();
+    }
     // Server MUST respond with Connection:keep-alive for us to enable it.
     // If we've been upgraded (via WebSockets) we also shouldn't try to
     // keep the connection open.
-    req.shouldKeepAlive = false;
+    if (!shouldKeepAlive) {
+      req.shouldKeepAlive = false;
+    }
   }
 
   if (req[kClientRequestStatistics] && hasObserver('http')) {
diff --git a/test/parallel/test-http-agent-exit.js b/test/parallel/test-http-agent-exit.js
new file mode 100644
index 00000000000..98be5b7eaac
--- /dev/null
+++ b/test/parallel/test-http-agent-exit.js
@@ -0,0 +1,53 @@
+'use strict';
+
+const common = require('../common');
+const cp = require('child_process');
+const http = require('http');
+
+if (process.argv[2] === 'server') {
+  const server = http.createServer((req, res) => {
+    if (req.method === 'HEAD') {
+      res.writeHead(200);
+      res.end();
+    } else if (req.url === '/204') {
+      res.writeHead(204);
+      res.end();
+    } else if (req.url === '/304') {
+      res.writeHead(304);
+      res.end();
+    }
+  });
+
+  server.listen(0, () => {
+    process.send(server.address().port);
+
+    // Unref server prior to final mustNotCall, server close will be prevented if sockets are still open
+    setTimeout(() => server.unref(), common.platformTimeout(1000));
+  });
+} else {
+  const serverProcess = cp.fork(__filename, ['server'], {
+    stdio: ['ignore', 'ignore', 'ignore', 'ipc']
+  });
+  serverProcess.once('message', common.mustCall((port) => {
+    serverProcess.channel.unref();
+    serverProcess.unref();
+    const agent = new http.Agent({ keepAlive: true });
+
+    // Make requests without consuming response
+    http.get({ method: 'HEAD', host: common.localhostIPv4, port, agent }, common.mustCall());
+    http.get({ method: 'GET', host: common.localhostIPv4, port, agent, path: '/204' }, common.mustCall());
+    http.get({ method: 'GET', host: common.localhostIPv4, port, agent, path: '/304' }, common.mustCall());
+
+    // Ensure handlers are called/not called as expected
+    const cb = common.mustCall((res) => {
+      res.on('end', common.mustCall());
+      res.on('data', common.mustNotCall());
+    }, 3);
+    http.get({ method: 'HEAD', host: common.localhostIPv4, port, agent }, cb);
+    http.get({ method: 'GET', host: common.localhostIPv4, port, agent, path: '/204' }, cb);
+    http.get({ method: 'GET', host: common.localhostIPv4, port, agent, path: '/304' }, cb);
+  }));
+
+  // HEAD, 204, and 304 requests should not block script exit
+  setTimeout(common.mustNotCall(), common.platformTimeout(3000)).unref();
+}