A header from Dan Gosling opened the scoring before second-half strikes from Charlie Daniels and Benik Afobe - Afobe's first ever Premier League goal - secured three points for the Cherries which saw them leapfrog the Canaries in the table.
Eddie Howe made one change to the starting line-up that were defeated by West Ham United in midweek, with Marc Pugh coming in while Lewis Grabban was unable to make the 18 due to illness.
Pugh, who replaced the injured Matt Ritchie, was tireless throughout and was instrumental in the Cherries’ opening two goals, the first of which came after just nine minutes.
The winger swung in a fantastic cross from the left and Gosling, who timed his run to perfection from deep, easily nodded in unmarked from five-yards to give the home side the lead.
Howe’s side were well on top and were denied a penalty just ten minutes later, when Daniels burst forward on the left and got beyond Russell Martin, but the Norwich skipper tugged back the full-back in the area. Referee Robert Madeley was unmoved despite vehement protests from the Cherries players and supporters.
Madeley was involved in a massive moment of the game again just three minutes before the break, as Harry Arter threaded a beautiful ball in behind for Afobe to chase and the striker got the first touch as goalkeeper Declan Rudd came steaming out.
The Norwich keeper clattered the former Wolves man on the edge of the box and after a lengthy period of deliberation, Madeley decided that only a yellow card was warranted for Rudd’s challenge, despite Afobe looking set to score.
But just a minute after the interval, the Cherries should have had their second when Pugh weaved his way through the Canaries defence and eventually got the ball onto his right-foot ten-yards out in the area, but the midfielder hit a low central effort which Rudd comfortably palmed away.
The Cherries winger didn’t stop there though and in the 52nd minute, won a penalty for his side as he got in behind and was pulled back by Vadis Odidja-Ofoe – this time Madeley had no hesitation in pointing to the spot.
Daniels stepped up with supreme confidence and hit a left-footed spot-kick which hit the right post but nestled into the net.
Norwich began to grow into the game but the Cherries hit them on the break and found a mesmerising third goal with 15 minutes to play.
Daniels picked the ball up on the left hand side and skinned two men before surging towards the byline and to round off his unbelievable piece of play, he swung in an inch-perfect cross into the box for Afobe to slot in from six-yards to make the three points safe for the Cherries.
Cherries: Boruc, Smith, Francis (c), Cook, Daniels, Stanislas, Gosling (Kermorgant 90), Surman, Arter (O'Kane 80), Pugh, Afobe (Murray 84).
Unused subs: Federici, Distin, MacDonald, Iturbe.
Norwich City: Rudd; Martin (c), Bennett, Bassong, Brady, Odjidja, Howson, Tettey, Jarvis, Hoolahan (Dorrans 69), Mbokani.
Unused subs: Ruddy, Wisdom, Olsson, Mulumbu.
Goals: Gosling (9), Daniels (54 (pen)), Afobe (75)
Attendance: 11,056 (1352 away fans)
Referee: R Madeley
Yellow cards: Rudd, Arter