QPR 0 Portsmouth 2
Marquis’ 76th-minute penalty put Pompey ahead and Harness sealed their win five minutes later.
Marquis tucked away the resulting spot-kick after being brought down by Toni Leistner.
And worse followed for the hosts when Ross McCrorie sprinted past Leistner on the left and laid the ball across to Harness, who applied the finish.
Marc Pugh had missed a great chance early in the second half, heading straight at Craig MacGillivray from Ryan Manning’s cross.
QPR almost scored a brilliant early goal.
A lovely team move started by keeper Liam Kelly – left out of the Scotland squad in favour of MacGillivray – led to Ilias Chair playing in Jan Mlakar, whose ball across the face of goal just evaded Bright Osayi-Samuel at the far post.
However, for all their neat approach play, Rangers were unable to break the deadlock and Pompey took full advantage after Leistner’s rash challenge.
QPR’s miserable night was summed up when a goal was initially given after Ebere Eze fired into the net in injury time, but the effort was disallowed after referee Ross Joyce consulted his assistant.
“Not good enough, simple as that. No excuses. We didn’t deserve to go through,” Warburton said.
“In the first 20-25 minutes we were very comfortable – probably too comfortable. We looked very good and then in truth we got complacent and sloppy.
“Portsmouth grew into the game and in the second half we flattered to deceive. We had lots of possession but that’s irrelevant because we never really troubled them.
“They then got the penalty and that changed it.”
On a more positive note for Rangers, Warburton praised young midfielder Charlie Owens for his performance.
Owens, picked up by the club after being released by Tottenham, was given his full debut.
Warburton said: “Young Charlie made his debut, which was fully deserved because he’s trained so well and for me I thought he was the stand-out performer for us tonight.
“I’m delighted for Charlie. But as a team we weren’t good enough.”
QPR: Kelly; Kane, Leistner, Barbet; Manning; Owens, Smith; Osayi-Samuel, (Eze 60) Chair (Wells 60), Pugh (Ball 75); Mlakar.
Subs not used: Barnes, Masterson, Scowen, Hugill.