diff --git a/lib/internal/http2/core.js b/lib/internal/http2/core.js
index eda587bc51e..9d3f9b84b7d 100644
--- a/lib/internal/http2/core.js
+++ b/lib/internal/http2/core.js
@@ -1034,7 +1034,7 @@ function setupHandle(socket, type, options) {
   // If the session has been destroyed, go ahead and emit 'connect',
   // but do nothing else. The various on('connect') handlers set by
   // core will check for session.destroyed before progressing, this
-  // ensures that those at l`east get cleared out.
+  // ensures that those at least get cleared out.
   if (this.destroyed) {
     process.nextTick(emit, this, 'connect', this, socket);
     return;
@@ -2126,7 +2126,7 @@ class Http2Stream extends Duplex {
   }
 
   [kProceed]() {
-    assert.fail('Implementors MUST implement this. Please report this as a ' +
+    assert.fail('Implementers MUST implement this. Please report this as a ' +
                 'bug in Node.js');
   }
 
@@ -3380,8 +3380,13 @@ function connect(authority, options, listener) {
 ObjectDefineProperty(connect, promisify.custom, {
   __proto__: null,
   value: (authority, options) => {
-    return new Promise((resolve) => {
-      const server = connect(authority, options, () => resolve(server));
+    return new Promise((resolve, reject) => {
+      const server = connect(authority, options, () => {
+        server.removeListener('error', reject);
+        return resolve(server);
+      });
+
+      server.once('error', reject);
     });
   },
 });
diff --git a/test/parallel/test-http2-client-promisify-connect-error.js b/test/parallel/test-http2-client-promisify-connect-error.js
new file mode 100644
index 00000000000..44ff4a28181
--- /dev/null
+++ b/test/parallel/test-http2-client-promisify-connect-error.js
@@ -0,0 +1,24 @@
+'use strict';
+
+const common = require('../common');
+
+if (!common.hasCrypto)
+  common.skip('missing crypto');
+const assert = require('assert');
+const http2 = require('http2');
+const util = require('util');
+
+const server = http2.createServer();
+
+server.listen(0, common.mustCall(() => {
+  const port = server.address().port;
+  server.close(() => {
+    const connect = util.promisify(http2.connect);
+    connect(`http://localhost:${port}`)
+      .then(common.mustNotCall('Promise should not be resolved'))
+      .catch(common.mustCall((err) => {
+        assert(err instanceof Error);
+        assert.strictEqual(err.code, 'ECONNREFUSED');
+      }));
+  });
+}));