Garry Monk made one change to his starting line-up, with Souleymane Doukara coming into the side for Hadi Sacko.
Graham Dorrans almost got Norwich off to a great start, he fired just wide from the edge of the box.
Doukara then did well to pick out Chris Wood in the box but he was unable to guide his header on target.
Kemar Roofe then went close for Leeds, space opened up for him on the edge of the box but he could only fire over.
A Pablo Hernandez free-kick gave Kyle Bartley an opportunity to head at goal, but he could only put the chance wide.
Kalvin Phillips then had a brilliant from range, which was only denied by a great save from Michael McGovern.
Against the run of play Norwich took the lead.
From a corner Robbie Brady looped a header at goal, Rob Green got to it, but he could only tip the ball on to Luke Ayling and the ball found its way into the back of the net.
Leeds looked for a response and almost got one through Wood.
Once again he combined with Doukara, but his volley was saved by McGovern.
Roofe was next to test McGovern, this time from a narrow angle, but he was unable to get the better of the Norwich stopper.
Half Time: Norwich City 1-0 Leeds United
After the break Leeds almost got an immediate response, Hernandez whipped in a cross to Roofe at the near post, but he could only head off target.
Leeds deservedly hit back in the 57th minute.
Wood won Leeds a corner and Pontus Jansson’s looping header found the top right corner sparking mass celebrations.
Five minutes later Green was called into action at a Robbie Brady free-kick where he made a good save.
At the other end Hernandez then showed great footwork to get a shot away from the edge of the box, but he couldn’t beat McGovern.
Leeds took the lead in the match for the first time with 16 minutes remaining.
Hadi Sacko showed desire to get to the byline, Eunan O'Kane played Ayling into the box and he teed up Wood to smash home.
Wood then almost sealed the points with four minutes remaining, his effort from the edge of the box went just wide, hitting the side netting.
Then in the 88th minute, Kyle Lafferty hit back for Norwich.
A superb lay-off on the chest by Cameron Jerome set the Northern Ireland striker up and he couldn’t be denied.
However there would be a winner for United.
Leeds had a free-kick 30 yards from goal, O'Kane laid the ball forward for Vieira and he smashed the ball into the bottom left corner with his first goal for the club, to secure Leeds all three points.
Full Time: Norwich City 2-3 Leeds United
Norwich: McGovern; Martin (c), Bennett, Klose, Olsson; Thompson; Brady (Ja Murphy 75), Dorrans, Hoolahan, Pritchard (Lafferty 84), Jerome. Subs not used: Ruddy, Bassong, Naismith, Oliveira, Jo Murphy.
Leeds: Green, Ayling, Jansson, Bartley, Taylor, Phillips, O’Kane, Hernandez (Grimes 89), Roofe (Sacko 55), Doukara (Vieira 72), Wood. Subs not used: Silvestri, Cooper, Antonsson, Berardi.
Booked: Phillips, Jansson (Leeds), Hoolahan, Jerome (Norwich)
Referee: A. Davies
Venue: Carrow Road