diff --git a/lib/net.js b/lib/net.js
index 4b3b96c8cd2736..6c523fcd214708 100644
--- a/lib/net.js
+++ b/lib/net.js
@@ -631,10 +631,20 @@ Socket.prototype.destroySoon = function() {
   if (this.writable)
     this.end();
 
-  if (this.writableFinished)
+  if (this.writableFinished && this.readableEnded)
     this.destroy();
   else
-    this.once('finish', this.destroy);
+    this.once('finish', () => {
+      // If we destroy the socket before we have received an incoming EOF
+      // the remote might still be sending data that will trigger a RST
+      // from this host once it is received
+      // Closing a TCP socket requires two FIN/ACK exchanges, one in every
+      // direction - this means two events
+      if (this.readableEnded)
+        this.destroy();
+      else
+        this.once('end', this.destroy);
+    });
 };
 
 
diff --git a/test/parallel/test-http-should-keep-alive.js b/test/parallel/test-http-should-keep-alive.js
index 038af47ee4db97..33fa46187040d6 100644
--- a/test/parallel/test-http-should-keep-alive.js
+++ b/test/parallel/test-http-should-keep-alive.js
@@ -49,7 +49,7 @@ const countdown = new Countdown(SHOULD_KEEP_ALIVE.length, () => server.close());
 const getCountdownIndex = () => SERVER_RESPONSES.length - countdown.remaining;
 
 const server = net.createServer(function(socket) {
-  socket.write(SERVER_RESPONSES[getCountdownIndex()]);
+  socket.end(SERVER_RESPONSES[getCountdownIndex()]);
 }).listen(0, function() {
   function makeRequest() {
     const req = http.get({ port: server.address().port }, function(res) {