diff --git a/lib/_stream_readable.js b/lib/_stream_readable.js
index 5b0972f2d73e5d..5edae5a5f7cc5d 100644
--- a/lib/_stream_readable.js
+++ b/lib/_stream_readable.js
@@ -818,7 +818,7 @@ Readable.prototype.unpipe = function(dest) {
     // remove all.
     var dests = state.pipes;
     state.pipes = [];
-    state.flowing = false;
+    this.pause();
 
     for (const dest of dests)
       dest.emit('unpipe', this, { hasUnpiped: false });
@@ -832,7 +832,7 @@ Readable.prototype.unpipe = function(dest) {
 
   state.pipes.splice(index, 1);
   if (state.pipes.length === 0)
-    state.flowing = false;
+    this.pause();
 
   dest.emit('unpipe', this, unpipeInfo);
 
diff --git a/test/parallel/test-stream-pipe-unpipe-streams.js b/test/parallel/test-stream-pipe-unpipe-streams.js
index 4cb8413af22f18..b1a673d9450ce8 100644
--- a/test/parallel/test-stream-pipe-unpipe-streams.js
+++ b/test/parallel/test-stream-pipe-unpipe-streams.js
@@ -84,3 +84,13 @@ assert.strictEqual(source._readableState.pipes.length, 0);
   checkDestCleanup(dest2);
   source.unpipe();
 }
+
+{
+  const src = Readable({ read: () => {} });
+  const dst = Writable({ write: () => {} });
+  src.pipe(dst);
+  src.on('resume', common.mustCall(() => {
+    src.on('pause', common.mustCall());
+    src.unpipe(dst);
+  }));
+}