Vale got off to a disastrous start after nine minutes when Mark Goodlad took too much time over a clearance resulting in Marc Nygaard closing the goalkeeper down and slotting home an easy finish.
The home side drew level 10 minutes later when Akpo Sodje's flick from a Danny Whitaker cross found Jeff Smith lurking at the back post where he fired an unstoppable half-volley past Jake Cole.
The Valiants rallied once more and took the lead in the 28th minute when Leon Constantine had a header denied by the crossbar only for Whitaker to follow up and smash the ball into an empty net.
Things almost went from bad to worse for the visitors when Cole's attempt to retrieve the ball from the edge of his area resulted in the goalkeeper fouling an advancing Constantine.
After consultation with his linesman, Cole was let off the hook as the referee judged the tackle to be a yard outside of his box only conceding a free-kick.
A poor start to the second half saw QPR trying their luck from range in the 51st minute when Nick Ward's promising run ended in the forward shooting wide of Goodlad's right post.
Richard Walker furthered his side's lead after 61 minutes when Danny Sonner's left-sided corner swung into the near post finding the head of the defender to send the ball into the top right of Cole's net.
The West London side's frustrations was summed up perfectly when, after failing to test the Vale backline with their forwards, it was left to centre-back Stefan Bailey to sky a shot poorly over the bar.
Rangers put themselves back in contention in the 78th minute when Lee Cook's right-sided free-kick was brilliantly saved by Goodlad only for Damion Stewart to pounce on the follow up from close range.
However, it proved to make little difference as Vale marched on to the third round for the first time in 10 years.