Barton rifled the home side ahead from 12 yards on 11 minutes, only to then see red after an apparent headbutt on Canaries midfielder Bradley Johnson.
Anthony Pilkington drew Norwich level just before half-time with a fine 20-yard effort, before substitute Steve Morison completed the turnaround with eight minutes left.
Canaries boss Paul Lambert always maintained this season would be all about his squad, and handed a Premier League debut to former St Mirren midfielder Simon Lappin.
QPR's defeat at Arsenal on New Year's Eve was a seventh in the last 10 games, with manager Neil Warnock expected to do plenty more business in this month's transfer window to arrest that slide as on-loan Manchester United striker Federico Macheda was named among the substitutes.
Norwich, playing in green, made a positive start, with Lappin's inswinging free-kick headed behind for an early corner.
Pilkington made a determined run through the heart of the home defence, but was eventually blocked as was the follow-up effort from Simeon Jackson, whose stoppage-time goal had earned a point against Fulham on Saturday.
QPR, though, took the lead with their first real attack on 11 minutes as Norwich again failed to keep a clean sheet.
The ball was pushed out to the left to Clint Hill, and his low centre travelled straight through the visitors defence, with Rangers captain Barton arriving on cue to fire his shot past John Ruddy from 12 yards.
Norwich had also fallen behind to an early goal against Fulham, and looked for a response as Johnson's 20-yard effort was deflected safely through to fit-again keeper Paddy Kenny.
Jackson failed to make a clean connection with a low ball into the QPR six-yard box, and stabbed his effort wide.
After 36 minutes, Barton lost his cool and following a tussle with Johnson appeared to headbutt the Norwich midfielder and was, after consultation with the assistant, shown a red card by referee Neil Swarbrick.
The visitors immediately went on the offensive, as Pilkington flashed a 20-yard strike wide.
On 43 minutes, the former Huddersfield winger drew Norwich level when he was given space again on the edge of the box - and this time drilled the ball into the bottom right corner.
QPR made a change for the second half when Shaun Wright-Phillips replaced Jamie Mackie.
The former Chelsea and Manchester City man was soon in the thick of the action, as Ruddy had to get down quickly to save his low shot.
On 53 minutes, Norwich centre-back Daniel Ayala upended Heidar Helguson to concede a free-kick 25-yards out.
Adel Taarabt got his effort up over the wall, and Ruddy had to make a fine reaction stop low to his right, touching the ball onto the post.
The visitors seemed happy to try to make their advantage count on the break, as Bennett tested Kenny with a 20-yard effort.
Norwich continued to look vulnerable at the back, as Zak Whitbread deflected another QPR shot behind for corner.
Lambert had seen enough, and made a treble substitution on 65 minutes as Morison replaced Grant Holt, Wes Hoolahan came on for Lappin and David Fox replaced full-back Adam Drury to leave just three in the rearguard.
Norwich had plenty of width as Whitbread glanced a header wide from Pilkington's left-wing cross.
Macheda replaced Helguson for the final 10 minutes.
It was, though, the visitors who would have the final say.
On 82 minutes, Morison blasted home from close range after Hoolahan had nodded down Pilkington's cross to leave Rangers just above the relegation zone and the Canaries back up in the top 10.