Lucas Moura gave Spurs the lead just before half time, but Aleksandar Mitrovic got Fulham back on level terms shortly after the break and the Cottagers looked the more likely to go on to win the game in North London.
However, a sensational free kick from Trippier and a well-taken effort from Kane - his first-ever goal in the Premier League during August - sealed a second successive triumph for Spurs and condemned Fulham to another defeat.
Spurs began the game on the front foot and should have been ahead after just six minutes, only for Moura to somehow head wide of the target from six yards out having been found by Ben Davies.
Fulham were attempting to play attacking football, but each time that they went forward it opened up more space for Spurs and Kane dragged a shot wide inside the area after seeing appeals for a penalty waved away by the referee.
Spurs responded with Eriksen seeing a low free kick well saved by Fabri, and Fulham soon went back up the other end as Ryan Sessegnon saw a shot smothered by Lloris at his feet after a perfectly-weighted pass from Jean Michael Seri.
However, Spurs finally got the goal that they deserved with two minutes of the first half remaining as Moura curled a shot into the far corner of the net from 20 yards after a Fulham clearance had fallen perfectly for him on the edge of the area.
Spurs had laid the foundations to push on for more goals after the restart, but it was Fulham who almost found an equaliser during the early stages of the second half as Mitrovic directed a 20-yard effort off the far post.
Dele Alli responded with a volley which was punched clear by Fabri, but Fulham quickly found their equaliser as Mitrovic headed home from close range after Sessegnon's miscued shot had gone straight to the Serbian in front of goal.
The Cottagers were beginning to look the more likely to edge ahead, and it resulted in Spurs head coach Mauricio Pochettino switching to a back four with Mousa Dembele being introduced for Davinson Sanchez.
The tactical switch proved key as Spurs dominated the closing half-an-hour, and Alli was only denied a goal when seeing a shot cleared off the line after Fabri had failed to deal with a cross.
Spurs eventually regained the lead with 16 minutes left, and in some style too, as Trippier - making his first appearance since the World Cup - curled a sublime free kick into the bottom corner from 30 yards out.
Fulham were left with little choice but to push men forward and it quickly led to Spurs finding a third through Kane, who finally netted his first Premier League goal in August by curling the ball into the far bottom corner after good work from Erik Lamela.
Spurs threatened to run riot as Kane and Alli both squandered chances from close range, with Fabri somehow managing to get his body in the way of the ball, but the misses did not prove costly as Fulham failed to mount any kind of a comeback.
Pochettino was able to introduce Harry Winks for his first top-flight appearance since December during the final minutes, and it capped a rewarding afternoon for Spurs who next travel to Manchester United.
TOTTENHAM HOTSPUR (3-4-2-1): Lloris; Alderweireld, Sanchez (Dembele 63'), Vertonghen; Trippier, Dier (Lamela 73'), Eriksen, Davies; Moura, Alli; Kane (Winks 89')
FULHAM XI (4-3-3): Fabri; Fosu-Mensah, Chambers, Le Marchand, Bryan (Christie 85'); Anguissa, Cairney (Johansen 73'), Seri; Kamara (Schurrle 88'), Sessegnon, Mitrovic body check tags ::