Albion have not lost this season when the former Arsenal striker has been on target. And they never looked likely to lose after he fired them ahead with a classy piece of finishing in the 23rd minute.
The Nigeria international, who was rested for the Boxing Day defeat at Manchester United, then put the game out of Tottenham's reach with his second seven minutes after half-time - taking his tally for the season to five.
The win also extended Albion's unbeaten home record to four games - collecting four clean sheets in the process.
Tottenham arrived riding high in fourth place but they looked anything but Champions League contenders as they meekly surrendered their hard won six-match unbeaten run.
They never got to grips with Albion's determined and up-tempo play, and even the non-stop effort of Jermain Defoe failed to secure a reward for Martin Jol's side.
After threatening to take the lead in only the third minute, when Defoe saw his drive blocked by Curtis Davies, Spurs were then forced to play much of the opening period on the back foot.
Visiting goalkeeper Paul Robinson was twice forced into saves to deny Nathan Ellington, before Albion made their pressure pay in the 23rd minute - thanks in no small part to a couple of fortunate ricochets.
The persistence of Ellington won the ball in midfield and he fed a pass into the path of Diomansy Kamara.
The Senegal international tussled for possession with Jermaine Jenas and the ball broke off Tottenham's England international midfielder and back towards his team-mate Michael Dawson.
Central defender Dawson was caught unawares and the ball rebounded off his foot in to the path of Kanu. He only had Robinson to beat and coolly strolled around the England international before sliding his shot into an empty net from an acute angle.
The only surprise was that Albion did not add to their advantage before half-time.
Despite their greater share of possession, the closest they came to increasing their advantage was when midfielder Ronnie Wallwork flashed a snap-shot wide on the half hour.
While Albion dominated the first-half, Tottenham still carried a major threat in Defoe.
The hosts were grateful to see his 44th-minute shot blocked after good work by Wayne Routledge.
It proved to be a vital intervention as Albion set the seal on their success after 52 minutes.
It was a goal earned by the determination of Kanu, who dispossessed central defender Anthony Gardner straight from a Tottenham throw in.
Gardner did his best to win the ball back, but Kanu easily shrugged off his challenge before powering forward to beat Robinson with a low drive at the near post.
Jol responded by sending on Robbie Keane, who has a habit of scoring against Albion, and Mido.
But even the introduction of the duo into a three-man frontline alongside Defoe could not breath any life into Tottenham's disappointing challenge.