The team from Carrow Road were always a threat but we just needed a break in front of goal when the game was finely balanced at 1-1.
Two minutes before Bennett's blast, Gareth Bale struck the underside of the crossbar and before that, John Ruddy produced a fantastic save to deny Benoit Assou-Ekotto.
But it wasn't to be - and the result means everything closes up further in the race to finish in the top four of the Premier League.
Harry Redknapp made five changes to the team that started at Sunderland on Saturday.
Aaron Lennon was back to start his first game in a month and was joined by Ledley King, Jake Livermore and a new strike partnership in Jermain Defoe and Louis Saha.
Emmanuel Adebayor, Rafa van der Vaart and Sandro were on the bench while Scott Parker and William Gallas missed out through injury.
Saha had the first effort on goal in the fourth minute but Norwich grew into the game and took the lead in the 13th minute.
Anthony Pilkington nicked the ball away from Younes Kaboul, Ledley King blocked Aaron Wilbraham but the ball broke back to Pilkington, who slotted home from 10 yards.
Russell Martin did well to block from a charging Bale and the full-back was there again to clear with Bale ready to pounce on Walker's cross.
Friedel tipped Pilkington's inswinging free-kick just wide and Defoe was inches away from Bale's low cross.
The equaliser arrived on 32 minutes. Walker won possession in the centre-circle, Livermore spotted Defoe's run in an instant and picked out the perfect pass for the striker to carry forward and clip over the advancing Ruddy.
Norwich almost had the final word though as another dangerous free-kick fell to centre-back Elliott Ward, who connected well with his volley but Friedel's reactions were up to the task.
We suffered an injury blow just before half-time as Kaboul limped off and was replaced by Ryan Nelsen and there was another change at the break as Adebayor was introduced for Saha.
Bale was denied by Ward's block inside a minute of the second half and then Ruddy somehow kept out Assou-Ekotto, throwing up a hand to divert the full-back's close-range effort after he'd played a one-two with Adebayor.
Bradley Johnson blasted a great chance wide in the 58th minute as the visitors became more and more of a threat on the counter as we pushed forward.
Bale was then inches away from what was always going to be the crucial next goal, his curler from the right corner of the box beat Ruddy but struck the underside of the crossbar and was cleared.
Two minutes later, and Bennett's thunderbolt ripped into the net from 20 yards.
Rafa van der Vaart was soon into the action for Livermore but we couldn't find another goal, the closest we came when Bale planted his header just wide from Assou-Ekotto's cross.
Spurs (4-4-2): Friedel; Walker, Kaboul (Nelsen, 45), King, Assou-Ekotto; Lennon, Livermore (van der Vaart, 71), Modric, Bale; Defoe, Saha (Adebayor, 46). Unused subs: Cudicini, Rose, Kranjcar, Sandro.
Norwich (4-4-2): Ruddy; Martin, R Bennett, Ward, Drury; E Bennett, Johnson, Howson, Pilkington (Surmon, 73); Holt (Morison, 69), Wilbraham (Jackson, 80). Unused subs: Steer, Crofts, Hoolahan, Barnett.
Goals: Spurs - Defoe (31); Norwich - Pilkington (13), E Bennett (66).
Referee: Mr M Oliver.
The winger blasted home an unstoppable drive in the 66th minute to clinch a 2-1 win for the Canaries.