The striker came on for Jermain Defoe after 72 minutes and superbly curled home a free-kick from 22 yards just four minutes later to vitally make the breakthrough.
Robbie Keane completed a satisfying afternoon with a typical piece of finishing in the final minute, beating Luis Boa Morte to a long ball, dancing around Edwin Van der Sar and tapping home.
It was no less than we deserved after dominating from start to finish although it looked like it could have been a frustrating afternoon until Kanoute's intervention.
Martin Jol made three changes with Mido starting up front with Defoe and a new-look left side with Andy Reid and Erik Edman both returning.
We dominated the first half without really carving Fulham open with Michael Brown's header cleared off the line the closest we came to breaking the deadlock.
There were no shortage of opportunities though with shots blocked or deflected and the final pass not always the best.
Stephen Kelly and Simon Davies enjoyed plenty of the ball down the right flank in the early stages but a Fulham defender always appeared in time to cut out the crosses.
Mido lashed a couple of shots wide and was closer with a 35-yard dipper after outfoxing Knight on Carrick's long clearance.
Brown's effort came in the 22nd minute as he rose well to meet Carrick's corner and his header was heading in until Boa Morte's intervention.
Reid and Mido tried their luck and Reid forced the save of the half on 27 minutes, a half-volley from 20 yards that Van der Sar saved spectacularly diving to his right.
Ledley King's header from another Carrick corner flew just wide before Fulham finally registered a shot, Diop's 30-yarder flying high a minute before the break.
The second half followed a very similar pattern. Mido, Davies and Noureddine Naybet all had efforts and appeals for a penalty were waved away when Defoe went over Knight's challenge.
Kanoute made his arrival after 72 minutes as Martin Jol went with two big men up front and four minutes later it had paid off. Clark brought down Reid, he was booked and as Van der Sar stood motionless, Kanoute curled the free-kick over the wall and into the far corner.
Robbie Keane came on for Mido with the celebrations still in full swing and soon combined with Reid, his blaster parried well by Van der Sar, before lashing inches over himself from 14 yards.
Diop had hearts in mouths when his volley dipped onto the roof of the net but Keane could have wrapped it up with three minutes left, missing the target from close range and then he did wrap it up, finishing superbly one-on-one after getting the better of Boa Morte in injury time.
GUIDE TO THE ACTION
2mins: Bright start by both sides, decent passing move between Davies and Defoe enabled Defoe to release Kelly down right flank, Bocanegra back just in time to block attempted cross.
3mins: Robinson out quickly to smother as Boa Morte tried to get onto Radzinski's pass.
4mins: Another break led by Davies, played it wide to Mido who cut in from right but dragged left-foot shot wide.
11mins: Defoe won 50-50 with Goma and fed Davies down right, early cross to Mido at far post, controlled but lashed wide.
13mins: Good work again between Davies and Kelly down right, Kelly's low cross cut out.
17mins: Mido got better of Knight from Carrick's long clearance, saw Van der Sar off line and tried early dipper from 35 yards, curled a couple of yards wide.
22mins: OFF LINE. Brown rose well to meet Carrick's corner, header cleared off line by Boa Morte.
24mins: Reid stepped inside Knight but 20-yarder blocked.
26mins: Mido fouled in winning header to release Defoe on goal but referee blew whistle straight away and called back play.
27mins: Builing up more pressure now, Mido turned away from Jensen and Knight, shot deflected for corner.
27mins: SAVE. Fulham struggled to clear corner, half-clearance hit by Reid on half-volley from 20 yards, Van der Sar flying save to pluck from top corner.
29mins: CLOSE. King diving header from Carrick's corner flicked off Knight and just wide.
44mins: Fulham's first effort of note, Diop 30-yarder sailed over.
Half-time: Spurs 0, Fulham 0
47mins: Reid did well to swivel and cross from left, Mido beat Knight to it but flicked header just wide.
50mins: Davies cut in from right, left foot shot flew over.
52mins: Mido twisted to reach Davies' flick on, no power on header.
58mins: Good defending by Bocanegra to head away Reid's deep cross for Davies. From corner, Naybet flick header from Reid's near-post inswinger just over.
58mins: SUB. John for Cole.
60mins: PENALTY? Defoe went over Knight's challenge in box but appeals waved away.
72mins: Davies skipped away from Bocanegra, early cross missed Mido and Rosenior managed to clear away from Reid in front of goal.
72mins: SUB. Kanoute for Defoe.
73mins: Edman shot across goal just needed touch but missed everyone.
76mins: YELLOW. Clark for foul on Reid.
77mins: GOAL. Van der Sar left standing in middle of goal as Kanoute's 22-yard free-kick nestled into far corner.
Spurs 1, Fulham 0
77mins: SUB. Keane for Mido.
79mins: SAVE. Van der Sar did well to beat out Reid's blaster from 16 yards, Keane failed to connect with rebound.,
80mins: BLOCK. Kelly superb tackle to block Boa Morte's shot as Fulham finally throw more caution to the wind.
84mins: CLOSE. Kanoute met Reid's cross, ball fell to Keane who drilled inches over from 14 yards.
85mins: SUB. McBride for Jensen.
87mins: CLOSE. Diop volley from Clark's free-kick landed on roof of net.
88mins: MISS. Keane sprinted in to meet Kanoute's cross from right but somehow missed target from six yards.
89mins: Keane tried his luck on volley from fully 40 yards with Van der Sar off line.
Injury time: GOAL. Keane got better of Boa Morte chasing ball over the top, danced around Van der Sar and tapped home.
Spurs 2, Fulham 0
Full-time: Spurs 2, Fulham 0
Spurs (4-4-2): Robinson, Kelly, Naybet, King, Edman; Davies, Carrick, Brown, Reid; Mido (Keane, 77), Defoe (Kanoute, 72). Subs: Cerny, Ziegler, Pamarot.
Fulham: Van der Sar, Bocanegra, Knight, Goma, Rosenior, Clark, Diop, Jensen (McBride, 85), Radzinski, Boa Morte, Cole (John, 58). Subs: Crossley, Volz, Legwinski.
Fredi Kanoute did the trick with his first touch as we finally broke Fulham's resistance to win Saturday's clash at the Lane.