diff --git a/lib/internal/debugger/inspect_client.js b/lib/internal/debugger/inspect_client.js
index 315617bf08a800..264e2743383972 100644
--- a/lib/internal/debugger/inspect_client.js
+++ b/lib/internal/debugger/inspect_client.js
@@ -13,7 +13,7 @@ const {
 const Buffer = require('buffer').Buffer;
 const crypto = require('crypto');
 const { ERR_DEBUGGER_ERROR } = require('internal/errors').codes;
-const { EventEmitter } = require('events');
+const { EventEmitter, once } = require('events');
 const http = require('http');
 const { URL } = require('internal/url');
 
@@ -343,13 +343,10 @@ class Client extends EventEmitter {
       this.emit('ready');
     };
 
-    return new Promise((resolve, reject) => {
-      this.once('error', reject);
-      this.once('ready', resolve);
-
-      httpReq.on('upgrade', handshakeListener);
-      httpReq.end();
-    });
+    const onReady = once(this, 'ready');
+    httpReq.on('upgrade', handshakeListener);
+    httpReq.end();
+    return onReady;
   }
 }
 
diff --git a/test/common/debugger.js b/test/common/debugger.js
index f5a47cbe06ea71..41d04fd67df64a 100644
--- a/test/common/debugger.js
+++ b/test/common/debugger.js
@@ -141,6 +141,10 @@ function startCLI(args, flags = [], spawnOpts = {}, opts = { randomPort: true })
       return getOutput();
     },
 
+    get stderrOutput() {
+      return stderrOutput;
+    },
+
     get rawOutput() {
       return outputBuffer.join('').toString();
     },
diff --git a/test/parallel/test-debugger-restart-message.js b/test/parallel/test-debugger-restart-message.js
index 190d0c18ccc081..292a15bd9f4d7a 100644
--- a/test/parallel/test-debugger-restart-message.js
+++ b/test/parallel/test-debugger-restart-message.js
@@ -31,6 +31,8 @@ const startCLI = require('../common/debugger');
     } finally {
       await cli.quit();
     }
+
+    assert.doesNotMatch(cli.stderrOutput, /MaxListenersExceededWarning/);
   }
 
   onWaitForInitialBreak();