A controversial penalty sparked an Arsenal revival that saw it move above Chelsea and Tottenham and into third place in the Premier League table.
Norwich, still worried about the prospect of relegation, was leading thanks to Michael Turner’s 56th minute opener when referee Mike Jones awarded Arsenal a penalty, ruling on the advice of a linesman that Kei Kamara had fouled Olivier Giroud.
With just five minutes remaining, Mikel Arteta converted that to set the stage for even later goals from Giroud and substitute Lukas Podolski, who had earlier hit the bar.
The visitors defended in numbers and restricted Arsenal to only a few crosses in the opening 20 minutes but City goalkeeper Mark Bunn had to be both brave and alert to deny Aaron Ramsey a few minutes later.
Arsenal came out in the second half with a barrage of pressure that Norwich somehow withstood, with Jack Wilshere seeing his shot blocked by Turner.
The ball hit the Norwich defender on an arm but referee Jones refused the inevitable appeals for a penalty.
Turner was immediately in the spotlight again at the other end when he lost his marker to head home Snodgrass’s free-kick from the right-hand corner of the box, with Lukasz Fabianski in the Arsenal goal, rooted to the spot as it went in.
Norwich’s luck finally ran out when referee Jones ruled that Kamara, defending a corner, had pulled Giroud down by the shirt and awarded a penalty, which was dispatched by Arteta with just five minutes remaining.
Arsenal threw everything at the visitors in the hope of three points and was rewarded when Alex Oxlade-Chamberlain, another substitute, played a one-two with Podolski and squared the ball across the Norwich goalmouth, where Giroud, arriving simultaneously with defender Bassong, turned it into the net. The Podolski turned to fire a low left-footer past Bunn in stoppage time.
Wigan in final
Wigan reached the FA Cup final for the first time after defeating Millwall 2-0 in the semifinals at Wembley on Saturday. Shaun Maloney netted the opening goal in the first half and Callum McManaman’s late strike finished off their Championship opponents.
The results: Aston Villa 1 drew with (N’Zogbia 55) Fulham 1 (Delph 66-og); Arsenal 3 (Arteta 85-pen, Bassong 88-og, Podolski 90) bt Norwich 1 (Turner 56); Everton 2 (Gibson 40, Anichebe 56) bt QPR 0; Reading 0 drew with Liverpool 0; Southampton 1 (Ramirez 59) drew with West Ham 1 (Carroll 66).