League leaders Pompey are now five points clear of Leicester, though it took a flurry of second half goals to settle the tie.
Following a quiet first-half in which neither side settled, the contest burst into life with five goals in just 15 minutes.
Yakubu Aiyegbeni (pictured) got the ball rolling for the home side when he beat the offside trap and chipped Robert Green in the visitors` net.
From the re-start The Canaries found themselves on level terms when Clint Easton tapped-home from Mark Rivers' cross.
Just two minutes later Svetoslav Todorov restored Pompey's lead, though Rivers crashed in a second equaliser moments after that.
With Portsmouth fans wondering if it would indeed be their night, Todorov stepped up and smacked in a winner after 72 minutes after Green failed to clear a corner from the left.
Elsewhere, Sheffield United followed up their FA Cup quarter final win over Leeds United with a 4-2 triumph over Burnley at Bramall Lane.
Free-scoring Michael Brown was the instigator behind The Blades` win, netting the club's first two goals to give Neil Warnock`s side a 2-0 half-time lead.
The Clarets did threaten a brief comeback when Gareth Taylor pulled a goal back after 64 minutes, though Peter Ndlovu ended the revival just minutes later.
Ndlovu proceeded add his second of the game late on, though Robbie Blake gave the visiting fans something to cheer about scoring in the last minute.
Wolverhampton strengthen their chances of achieving a play-off spot following a hard-fought 1-0 win over Reading at the Madejski Stadium.
Reading would have cemented their own play-off ambitions with a win, and closed in on Leicester, but failed to recover from Shaun Newton's goal just before the break.
In an even match Nathan Blake was unlucky not to score himself when his shot hit the post just before the break, however Newton, along with Kenny Miller, followed in the shot and stabbed home.
Click here for Division One match summaries:
Portsmouth 3-2 Norwich
Reading 0-1 Wolves
Sheff Utd 4-2 Burnley
Click here for the latest Division One table.
