diff --git a/lib/_stream_readable.js b/lib/_stream_readable.js
index dfba99cbc74d7d..39a7ec8d93ad53 100644
--- a/lib/_stream_readable.js
+++ b/lib/_stream_readable.js
@@ -499,10 +499,13 @@ Readable.prototype.pipe = function(dest, pipeOpts) {
     src.once('end', endFn);
 
   dest.on('unpipe', onunpipe);
-  function onunpipe(readable) {
+  function onunpipe(readable, unpipeInfo) {
     debug('onunpipe');
     if (readable === src) {
-      cleanup();
+      if (unpipeInfo && unpipeInfo.hasUnpiped === false) {
+        unpipeInfo.hasUnpiped = true;
+        cleanup();
+      }
     }
   }
 
@@ -628,6 +631,7 @@ function pipeOnDrain(src) {
 
 Readable.prototype.unpipe = function(dest) {
   var state = this._readableState;
+  var unpipeInfo = { hasUnpiped: false };
 
   // if we're not piping anywhere, then do nothing.
   if (state.pipesCount === 0)
@@ -647,7 +651,7 @@ Readable.prototype.unpipe = function(dest) {
     state.pipesCount = 0;
     state.flowing = false;
     if (dest)
-      dest.emit('unpipe', this);
+      dest.emit('unpipe', this, unpipeInfo);
     return this;
   }
 
@@ -662,7 +666,7 @@ Readable.prototype.unpipe = function(dest) {
     state.flowing = false;
 
     for (var i = 0; i < len; i++)
-      dests[i].emit('unpipe', this);
+      dests[i].emit('unpipe', this, unpipeInfo);
     return this;
   }
 
@@ -676,7 +680,7 @@ Readable.prototype.unpipe = function(dest) {
   if (state.pipesCount === 1)
     state.pipes = state.pipes[0];
 
-  dest.emit('unpipe', this);
+  dest.emit('unpipe', this, unpipeInfo);
 
   return this;
 };
diff --git a/test/parallel/test-stream-pipe-same-destination-twice.js b/test/parallel/test-stream-pipe-same-destination-twice.js
new file mode 100644
index 00000000000000..1824c0606451a2
--- /dev/null
+++ b/test/parallel/test-stream-pipe-same-destination-twice.js
@@ -0,0 +1,78 @@
+'use strict';
+const common = require('../common');
+
+// Regression test for https://github.com/nodejs/node/issues/12718.
+// Tests that piping a source stream twice to the same destination stream
+// works, and that a subsequent unpipe() call only removes the pipe *once*.
+const assert = require('assert');
+const { PassThrough, Writable } = require('stream');
+
+{
+  const passThrough = new PassThrough();
+  const dest = new Writable({
+    write: common.mustCall((chunk, encoding, cb) => {
+      assert.strictEqual(`${chunk}`, 'foobar');
+      cb();
+    })
+  });
+
+  passThrough.pipe(dest);
+  passThrough.pipe(dest);
+
+  assert.strictEqual(passThrough._events.data.length, 2);
+  assert.strictEqual(passThrough._readableState.pipesCount, 2);
+  assert.strictEqual(passThrough._readableState.pipes[0], dest);
+  assert.strictEqual(passThrough._readableState.pipes[1], dest);
+
+  passThrough.unpipe(dest);
+
+  assert.strictEqual(passThrough._events.data.length, 1);
+  assert.strictEqual(passThrough._readableState.pipesCount, 1);
+  assert.strictEqual(passThrough._readableState.pipes, dest);
+
+  passThrough.write('foobar');
+  passThrough.pipe(dest);
+}
+
+{
+  const passThrough = new PassThrough();
+  const dest = new Writable({
+    write: common.mustCall((chunk, encoding, cb) => {
+      assert.strictEqual(`${chunk}`, 'foobar');
+      cb();
+    }, 2)
+  });
+
+  passThrough.pipe(dest);
+  passThrough.pipe(dest);
+
+  assert.strictEqual(passThrough._events.data.length, 2);
+  assert.strictEqual(passThrough._readableState.pipesCount, 2);
+  assert.strictEqual(passThrough._readableState.pipes[0], dest);
+  assert.strictEqual(passThrough._readableState.pipes[1], dest);
+
+  passThrough.write('foobar');
+}
+
+{
+  const passThrough = new PassThrough();
+  const dest = new Writable({
+    write: common.mustNotCall()
+  });
+
+  passThrough.pipe(dest);
+  passThrough.pipe(dest);
+
+  assert.strictEqual(passThrough._events.data.length, 2);
+  assert.strictEqual(passThrough._readableState.pipesCount, 2);
+  assert.strictEqual(passThrough._readableState.pipes[0], dest);
+  assert.strictEqual(passThrough._readableState.pipes[1], dest);
+
+  passThrough.unpipe(dest);
+  passThrough.unpipe(dest);
+
+  assert.strictEqual(passThrough._events.data, undefined);
+  assert.strictEqual(passThrough._readableState.pipesCount, 0);
+
+  passThrough.write('foobar');
+}