Premier League - Barton sent off as Norwich beat QPR
Barton's slick finish gave QPR an 11th-minute lead before he was dismissed for a head-butt on Bradley Johnson.
Norwich made the extra man count almost immediately, equalising before half-time through Anthony Pilkington's unstoppable long-range effort.
The visitors pushed for a winner and it eventually came via substitute Morison, who lashed in from close range to complete an impressive comeback.
QPR came into this game on the back of a wretched run of home form that has now seen them win just one of their last 10 matches at Loftus Road.
Manager Neil Warnock has made clear the need to add to their squad this month to consolidate the club's Premier League status.
Playing to a high tempo for much of the first period, QPR had Norwich on the back foot - so it was not undeserved when they took the lead through Barton.
Running on to Clint Hill's intelligent hooked cross from the left, the skipper drilled in with aplomb.
But Barton, who had been the subject of a couple of hefty Norwich challenges, snapped in the 36th minute. After tangling with Johnson, Barton reacted with an ill-advised head-butt.
While it may have been more petulant than violent, referee Neil Swarbrick was well within his rights to dismiss the former Newcastle midfielder for the fifth time in his career.
Norwich, visibly lifted by Barton's sending off, responded with the equaliser six minutes later.
Bursting into space behind Shaun Derry, Pilkington unleashed an unstoppable left-footed drive from 25 yards that nestled in the bottom corner.
Predictably Norwich were on top in the second half, but struggled to create clear chances.
Instead it was Adel Taarabt, impressive throughout, who forced John Ruddy into palming the ball on to his post after the Moroccan's free-kick seemed destined for the back of the net.
The introduction of Shaun Wright-Phillips caused Norwich a few problems, but Paul Lambert's side rarely looked troubled by anyone other than Taarabt.
But Taarabt's influence waned after Lambert's inspired triple substitution in the 66th minute.
The introductions of David Fox, Wes Hoolahan and Morison stretched QPR's tired legs and Norwich eventually went ahead seven minutes from the end.
Pilkington's deep cross from the left was headed back into the danger zone by Elliott Bennett, allowing Morison the space to sweep in from close range.
Boos rang out around Loftus Road at the full-time whistle, but it is QPR's captain - not referee Swarbrick - who takes the blame for defeat.