Against the run of play in the first-half, Fabio Borini converted a penalty that he had won just before half-time, and the visitors never looked back.
Norwich pressed high once more and the Black Cats punished them once more, Borini’s cross found Jermain Defoe, who slid in at the back post to put the ball in the net.
Duncan Watmore rounded off the scoring in injury time, Seb Larsson slotted through to the youngster, who made no mistake after taking the ball round the keeper.
Who impressed during a memorable day for Allardyce’s side? Let's rate them out of 10.
Outstanding performance from the back five
Vito Mannone (8 out of 10) – Second clean-sheet in three game, Mannone produced excellent saves from Martin Olsson, Nathan Redmond and even denied his own play from putting into his own net.
DeAndre Yedlin (7 out of 10) – Yedlin took a nasty blow to the head when he was pushed into the advertising boarding, but despite that he continued strongly and helped going forward.
Lamine Kone (7 out of 10) – Arguably Kone’s best performance in a Sunderland’s shirt, he was solid and never looked likely to crack under the intense pressure of the game.
Younes Kaboul (8 out of 10) – Just like his partner at the back, Kaboul barely stepped out of line, and Dieumerci Mbokani’s threat was wiped out from the start by the centre-half.
Patrick van Aanholt (7 out of 10) – Looked to get forward and join in with the counter-attacks, but never looked likely to make a mistake at the back and nullified the Matt Jarvis threat all game.
Sheer brilliance in midfield
Lee Cattermole (8 out of 10) – Questions have been asked of ‘Cats’ in recent weeks, but what you get from him is a lot of heart and fight, and he showed exactly that as he seemed to thrive on the pressure of the occasion.
Jan Kirchhoff (8 out of 10) – Looked at home alongside Cattermole in the middle of the park, another brilliant display from the German, who sat in front of the back four all game and made a big impact on the team.
Yann M’Vila (7 out of 10) – Just like his two midfield compatriots, M’Vila worked hard all afternoon, and cut out attacks before they could really develop.
Two of front three stood out
Fabio Borini (7 out of 10) – First impact of the match came on 40 minutes when he won and slotted home the penalty, and he also bagged an assist when he found Defoe for the second goal.
Jermain Defoe (7 out of 10) – Defoe scored Sunderland’s second goal of the game, which settled any nerves and questions hanging over them, he may well have had a couple more though.
Wahbi Khazri (5 out of 10) – Not the best of displays from Khazri, picked up a booking and was replaced at half-time by Watmore, who went on to stake a claim for a start.
Impact from the substitutes
Duncan Watmore (7 out of 10) – Allardyce said that the youngster had only been training with the side for four days, and what a comeback he made. After replacing Khazri, he went on to score the third goal in the game
Seb Larsson (7 out of 10) – Just like Watmore, Larsson has been out for a while, and he went on to claim an assist for the third goal after a neat pass set up the youngster. Replaced M’Vila midway through the second-half.
John O’Shea (6 out of 10) – Allardyce wanted to protect his two-goal lead, so O’Shea came on in place of Kirchhoff with five minutes to go, and he managed to help his side see the game out.