Martin Jol's side came into the game having gone 433 minutes without scoring, but produced a gutsy performance to see off a Portsmouth side who had enjoyed an impressive start to the Premiership campaign.
Murphy fired Tottenham in front after just 39 seconds, before Defoe fired home from the penalty spot in controversial circumstances.
Didier Zokora clearly dived inside the area, but referee Chris Foy still awarded the penalty which proved to be the all-important matchwinner for the home side.
Kanu pulled a goal back for Portsmouth just before half-time but Tottenham held on to record only their second victory of the season.
All eyes were focused on the return of Portsmouth defender Sol Campbell to White Hart Lane.
Tottenham fans refuse to forgive the England defender for making a move to arch rivals Arsenal back in 2001 and made it a hate-filled return for the experienced defender.
And Campbell was to suffer immediate heartache when Tottenham opened the scoring after just 39 seconds of the game.
Defoe's cross picked out Dimitar Berbatov whose downward header was only parried by David James in the Portsmouth goal.
The rebound fell nicely to Murphy and he made no mistake firing the ball into the back of the net.
Murphy could have added his second of the game on 14 minutes when he created space for himself on the edge of the box and curled a sweet shot which produced a superb save from James diving away to his right.
Portsmouth created their first clear cut opportunity of the match on 19 minutes when Gary O'Neil's fired a powerful drive straight into the path of Paul Robinson.
As well as putting up with a barrage of abuse from the home supporters, Campbell was also facing a difficult task in keeping Defoe quiet.
Defoe got the better of Campbell on 23 minutes when he turned him on the edge of the area and drilled a low powerful shot which was well saved by James diving low to his left.
But the England forward finally got his just rewards when he added a second from the penalty spot on 35 minutes.
Former Tottenham midfielder Pedro Mendes was adjudged to have tripped Zokora inside the area, but television replays clearly showed that there was no contact made.
Referee Foy had other ideas and had no hesitation in awarding the penalty and Defoe fired the spot-kick into the corner of the net for his first goal of the season.
Portsmouth refused to lie down and got themselves back into the game on 40 minutes.
O'Neil's cross from the right picked out Kanu who directed a close-range header past Robinson into the top left hand corner of the net.
Michael Dawson produced a superb diving header to block Niko Kranjcar's powerful shot which looked destined for the back of the net on 57 minutes.
And the Croatian midfielder came close again for Portsmouth on 65 minutes when he fired a fierce drive which flew just over the crossbar.
Jermaine Jenas was desperately unlucky not to get his name on the scoresheet on 70 minutes.
Jenas unleashed a blistering shot from the edge of the box which produced a superb save from James diving away to his left.
Robinson showed why he is England's number one when he produced a fantastic reflex save to deny Lomana LuaLua in injury time and ensure three points for the home side.