Despite falling behind to an early header from Kanu, Defoe ensured Tottenham booked a home tie against Nottingham Forest next Saturday.
Head coach Martin Jol signalled his intentions from the start by naming an attacking line-up with Defoe, Robbie Keane and Fredi Kanoute all starting for the first time since he took over the managerial reins.
West Brom were missing the cup-tied Kieran Richardson and Jonathan Greening through injury, but manager Bryan Robson was able to recall Martin Albrechtsen to the starting line-up.
And it was the Premiership strugglers who created the first clear-cut opportunity of the game after just three minutes.
Ricardo Scimeca found space for himself in the Tottenham half and fired a 30-yard drive which flew just over the crossbar.
The Baggies continued to mount all the early pressure and broke the deadlock after 12 minutes when former Arsenal striker Kanu silenced the home supporters who had been giving him abuse.
Zoltan Gera broke free down the right-hand side and delivered a superb cross for Kanu who made no mistake heading the ball past Paul Robinson into the corner of the net.
Robinson then produced two wonder saves to keep his side in the tie.
Jason Koumas released Kevin Campbell into the box, but the West Brom skipper saw his close-range shot well beaten out by Robinson.
And the England keeper had to be at his best again just sixty seconds later when Kanu played a delicate ball into the path of defender Paul Robinson.
The Baggies man struck a sweet shot with the outside of his boot, but the Spurs keeper once again produced a superb save diving away to his right.
Tottenham were hanging on for their lives and Campbell should have made it two for West Brom on 34 minutes.
Gera was involved in the heart of the action once again and played Campbell through on goal, but the former Arsenal star saw a blistering shot turned round the post by Robinson.
Tottenham had to wait until the 37th minute before creating their first chance of the game. Kanoute broke away down the right and played the ball into Defoe.
And even though the England star found himself completely unmarked inside the box, he could only volley the ball high over the crossbar.
But the home side were awarded a controversial penalty after 45 minutes. Michael Carrick played Stephen Kelly into the box and the referee adjudged he was brought down by Russell Hoult, even though Hoult injured himself going for the ball.
The West Brom keeper had to be replaced by substitute keeper Tomasz Kuszczak, but referee Rob Styles had no hesitation in pointing to the spot.
Striker Robbie Keane made no mistake firing the spot-kick into the corner of the net.
And how that decision would come back to haunt West Brom as Tottenham looked a totally different outfit in the second half.
A piece of magic from Defoe on 50 minutes put the home side into the lead. Tottenham were awarded a free-kick on the edge of the box.
Michael Carrick played a short ball for the prolific forward who unleashed an unstoppable drive which flew past Kuszczak into the back of the net.
And Defoe was quick to add his second and Tottenham's third in the 55th minute when Kanoute raced to the byline and cut the ball back for the young star.
Defoe neatly controlled it before coolly slotting the ball past Kuszczak into the corner of the net and securing Tottenham's place in the next round.
Man of the match: Jermain Defoe
Only one winner as Defoe again showed the watching Sven-Goran Eriksson why he is one of the best strikers in the English game.