Kane grabbed the only goal of a dull affair in west London with a trademark finish on the stroke of half-time when he turned away from Tim Ream and curled into the bottom corner.
It was Kane’s 266th goal for the club and moved him level with Jimmy Greaves, whose tally has stood since 1970, as Spurs’ all-time record scorer.
Trophies, however, continue to evade the 29-year-old, whom Conte revealed played on Monday night despite being unwell.
“Today he was amazing. I think he scored a fantastic goal, the execution, to control the ball, then to kick it in that way, only a world-class striker can score this goal,” Conte said.
“About the spirit that I spoke before, I want to underline Harry played with a fever and he was not so good, but he wanted to play because he understood the moment.
“He understood he is a point of reference for us, for me, for the other players and, with (goalkeeper) Hugo (Lloris), they are the two players who are a point of reference for the dressing room. Today I am really happy because I think he was rewarded with a goal.
“For sure, I would like to help him and me, also his team-mates, to try to do something important, to win something with Tottenham because he loves Tottenham.
Tottenham is in his heart and it should be good if together we were able to win something
Antonio Conte on Harry Kane
“Tottenham is in his heart and it should be good if together we were able to win something, because then it is important to have this record, but I think it could be more important if you win a trophy.”
Kane said in a video clip on Tottenham’s Twitter account he was “really proud” to equal Greaves’ record.
Victory at Craven Cottage ended a difficult period for Spurs, who lost 4-2 at Manchester City on Thursday night and 24 hours later discovered sporting director Fabio Paratici had been hit with a 30-month ban relating to financial irregularities during his time at Juventus.
Paratici’s suspension currently only applies to Italy and he is awaiting the written reasons before any decision is made over an appeal.
A day later and a small band of supporters protested outside the club’s Enfield-based training ground calling for owners ENIC and chairman Daniel Levy to leave.
Further calls for Levy to depart Tottenham were heard throughout the 1-0 win at Fulham, which moved Spurs to within three points of third place.
Conte added: “It was a good answer. After defeats to Arsenal and Manchester City, first and second in the table, I asked my players to show characteristics from last season.
“The will, the desire and to suffer in the moments you have to suffer. Today we didn’t suffer a lot, but I have seen they are ready so it could be a starting point for us.
“Don’t forgot we played against a team who are a real surprise this season, with a win they could overcome us in the table, to win away here is not easy.
“For this reason I am really happy because I repeat I saw again the characteristics that brought us last season a place in the Champions League.”
Fulham boss Marco Silva was left frustrated after his side’s first-half dominance failed to translate into a positive result.
He also felt Son Heung-min could have been shown a red card for a tackle on Kenny Tete in the 28th minute when he caught the home defender high on the ankle.
“Yes, I saw it and I thought it could be more than a yellow card in that moment,” Silva said.
“Of course Kane is a decider, he is a great footballer as well, but we were controlling it and we were punished by a great finish by him.”