The 17-year-old's strike meant that Rangers are now unbeaten in four as their resurgence under Gary Waddock continues.
Both teams started brightly despite playing in a half-empty Loftus Road, but it was the League One visitors who had the first chance after six minutes. Former Scotland international Eoin Jess delivered a nice weighted ball to the back post which James Quinn chested down and fired straight at Jake Cole.
But when Rangers had the ball they looked the most threatening and, although a number of key players were missing, they had enough class to take control.
One of the club's bigger names, Lee Cook, fired just wide with a sweet shot from 20 yards on 12 minutes and captain Kevin Gallen headed a Dexter Blackstock cross just past the near post four minutes later.
It was the in-form Cook and Blackstock who combined for the opener after 18 minutes, when the former Southampton striker chased down a long ball and laid it back for the on-rushing winger.
Cook took it in his stride and although his low shot hit defender Luke Chambers the deflection was enough to take it past a despairing Mark Bunn.
The home side took their foot off the gas a little towards the end of the half as their opponents finished it the strongest. Rangers defender Zesh Rehman nearly put through his own net on 40 minutes before Andy Kirk was allowed to race onto a Jason Crowe through ball and hit the post.
However Waddock's men settled down after the break and it took just three minutes for them to double their lead. Gallen stepped up to take a free-kick to the left of the penalty area and swung a low shot into Bunn's far corner.
However, celebrations were short lived when Cobblers substitute Jerome Watt, making his first-team debut, hit a low shot from 25 yards which Cole could not get down to quick enough.
Although QPR continued to pepper Bunn's goal with long-range efforts, the damage had been done and Northampton were able to equalise with 12 minutes remaining.
A free-kick bounced up in the air and Jess met the ball unchallenged to head down to Kirk who hit a sweet volley on the turn into the far corner.
But it was substitute Jones who came to the rescue two minutes from time with a looping header from a Marcus Bignot cross to win it for Rangers.