Joe Gallen basked in a ‘deserved’ victory as Pompey claimed another Championship scale.
QPR joined Birmingham on the sidelines as the Blues’ Carabao Cup progress continued.
John Marquis and Marcus Harness netted in the final 13 minutes to secure a superb 2-0 triumph at Loftus Road.
That win ensures Kenny Jackett’s side will now host fierce rivals Southampton at Fratton Park in the third round.
And the Blues’ assistant manager was delighted with their display over Mark Warburton’s Championship opposition.
Gallen said: ‘I think overall we deserved it.
‘For the opening 20 minutes, QPR played very well, although I can’t remember a chance, a shot on target or a clear-cut moment.
‘We did think if we could win the toss and make them kick towards the Loft End that could be important. I’ve been here many a time to know that is a way of winning, it’s not everything but it does help.
‘The feeling was if we could see that opening 20 minutes out then the game may settle and we could grow in confidence and get our football going, get up the pitch and get some chances.
‘When it gets into the 70th minute it is first goal wins really – luckily for us we got a penalty and I thought it was a penalty .
‘You could see after the first goal a lot of confidence came flooding back to our team.
‘The second goal was very good and Ross (McCrorie) does have the athleticism and quality to stride forward from midfield.
‘Then you are thinking has he enough composure and quality to roll the ball across the box – and he did.’