diff --git a/lib/_stream_readable.js b/lib/_stream_readable.js
index 338bf2a7539bfc..275691cbb2e805 100644
--- a/lib/_stream_readable.js
+++ b/lib/_stream_readable.js
@@ -538,9 +538,9 @@ Readable.prototype.pipe = function(dest, pipeOpts) {
       // If the user unpiped during `dest.write()`, it is possible
       // to get stuck in a permanently paused state if that write
       // also returned false.
-      if (state.pipesCount === 1 &&
-          state.pipes[0] === dest &&
-          src.listenerCount('data') === 1 &&
+      // => Check whether `dest` is still a piping destination.
+      if (((state.pipesCount === 1 && state.pipes === dest) ||
+           (state.pipesCount > 1 && state.pipes.indexOf(dest) !== -1)) &&
           !cleanedUp) {
         debug('false write response, pause', src._readableState.awaitDrain);
         src._readableState.awaitDrain++;
diff --git a/test/parallel/test-stream-pipe-await-drain.js b/test/parallel/test-stream-pipe-await-drain.js
new file mode 100644
index 00000000000000..fba99ed4563c14
--- /dev/null
+++ b/test/parallel/test-stream-pipe-await-drain.js
@@ -0,0 +1,40 @@
+'use strict';
+const common = require('../common');
+const stream = require('stream');
+
+// This is very similar to test-stream-pipe-cleanup-pause.js.
+
+const reader = new stream.Readable();
+const writer1 = new stream.Writable();
+const writer2 = new stream.Writable();
+
+// 560000 is chosen here because it is larger than the (default) highWaterMark
+// and will cause `.write()` to return false
+// See: https://github.com/nodejs/node/issues/5820
+const buffer = Buffer.allocUnsafe(560000);
+
+reader._read = function(n) {};
+
+writer1._write = common.mustCall(function(chunk, encoding, cb) {
+  this.emit('chunk-received');
+  cb();
+}, 1);
+writer1.once('chunk-received', function() {
+  setImmediate(function() {
+    // This one should *not* get through to writer1 because writer2 is not
+    // "done" processing.
+    reader.push(buffer);
+  });
+});
+
+// A "slow" consumer:
+writer2._write = common.mustCall(function(chunk, encoding, cb) {
+  // Not calling cb here to "simulate" slow stream.
+
+  // This should be called exactly once, since the first .write() call
+  // will return false.
+}, 1);
+
+reader.pipe(writer1);
+reader.pipe(writer2);
+reader.push(buffer);