diff --git a/plugins/node/instrumentation-undici/test/undici.test.ts b/plugins/node/instrumentation-undici/test/undici.test.ts
index aea2f036ce..c125b2e189 100644
--- a/plugins/node/instrumentation-undici/test/undici.test.ts
+++ b/plugins/node/instrumentation-undici/test/undici.test.ts
@@ -119,6 +119,10 @@ describe('UndiciInstrumentation `undici` tests', function () {
     propagation.disable();
     mockServer.mockListener(undefined);
     mockServer.stop(done);
+
+    // Close kept-alive sockets. This can save a 4s keep-alive delay before the
+    // process exits.
+    (undici as any).getGlobalDispatcher().close();
   });
 
   beforeEach(function () {
@@ -216,11 +220,27 @@ describe('UndiciInstrumentation `undici` tests', function () {
       };
 
       const queryRequestUrl = `${protocol}://${hostname}:${mockServer.port}/?query=test`;
-      const firstQueryResponse = await undici.request(queryRequestUrl, {
-        headers,
-        // @ts-expect-error - method type expects in uppercase
-        method: 'get',
-      });
+      let firstQueryResponse;
+      try {
+        firstQueryResponse = await undici.request(queryRequestUrl, {
+          headers,
+          // @ts-expect-error - method type expects in uppercase
+          method: 'get',
+        });
+      } catch (err: any) {
+        // This request is using a bogus HTTP method `get`. If (a) using Node.js
+        // v14, v16, or early v18.x versions and (b) this request is re-using
+        // a socket (from an earlier keep-alive request in this test file),
+        // then Node.js will emit 'end' on the socket. Undici then throws
+        // `SocketError: other side closed`.  Given this is only for old Node.js
+        // versions and for this rare case of using a bogus HTTP method, we will
+        // skip out of this test instead of attempting to fully understand it.
+        assert.strictEqual(err.message, 'other side closed');
+        this.skip();
+      }
+      if (!firstQueryResponse) {
+        return;
+      }
       await consumeResponseBody(firstQueryResponse.body);
 
       const secondQueryResponse = await undici.request(queryRequestUrl, {