diff --git a/core/packages/teeny-request/src/index.ts b/core/packages/teeny-request/src/index.ts
index 931861ad798c..313e4ab101a0 100644
--- a/core/packages/teeny-request/src/index.ts
+++ b/core/packages/teeny-request/src/index.ts
@@ -278,10 +278,18 @@ function teenyRequest(
     let responseStream: any;
     requestStream.once('reading', () => {
       if (responseStream) {
-        pipeline(responseStream, requestStream, () => {});
+        if (!requestStream.destroyed) {
+          pipeline(responseStream, requestStream, () => {});
+        } else if (responseStream && typeof responseStream.destroy === 'function') {
+          responseStream.destroy();
+        }
       } else {
         requestStream.once('response', () => {
-          pipeline(responseStream, requestStream, () => {});
+          if (!requestStream.destroyed) {
+            pipeline(responseStream, requestStream, () => {});
+          } else if (responseStream && typeof responseStream.destroy === 'function') {
+            responseStream.destroy();
+          }
         });
       }
     });
diff --git a/core/packages/teeny-request/test/index.ts b/core/packages/teeny-request/test/index.ts
index e34d697a2a58..a7e4cb3de4f1 100644
--- a/core/packages/teeny-request/test/index.ts
+++ b/core/packages/teeny-request/test/index.ts
@@ -298,6 +298,25 @@ describe('teeny', () => {
     });
   });
 
+  it('should not pipe if request stream is destroyed early', done => {
+    const scope = mockJson();
+
+    const stream = teenyRequest({uri});
+    stream.on('error', done);
+
+    stream.once('response', response => {
+      response.body.once('close', () => {
+        scope.done();
+        done();
+      });
+
+      // Destroy the stream before piping can be fully set up
+      stream.destroy();
+    });
+
+    stream.resume();
+  });
+
   it('should expose TeenyStatistics instance', () => {
     assert.ok(teenyRequest.stats instanceof TeenyStatistics);
   });