Kane struck his 266th Tottenham goal to seal a vital 1-0 win at Craven Cottage which keeps the North London club firmly in the hunt for a top-four Premier League finish.
England captain Kane netted on the stroke of half time with a clinical strike from the edge of the penalty area to move level with the great Jimmy Greaves.
It was the 29-year-old's first goal in three games and also moved him to within one goal of joining Alan Shearer and Wayne Rooney in the 200-goals Premier League club.
Conte revealed after the match that Kane played despite being ill with a fever and that it was that kind of fighting spirit that inspires him to want to help the player – Kane has never won a major trophy for club or country – win silverware.
But Conte said: "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.
"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 sure, I would like to help him and me, also his teammates, 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, because then it is important to have this record, but I think it could be more important if you win a trophy."
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Kane has the chance to move out on his own as the club's record scorer in the FA Cup on Saturday when Spurs take on Championship side Preston North End.
Greaves' record has stood since 1970. He died aged 81 in 2021 and is widely regarded as one of the greatest goalscorers in history.
Kane's 18th goal in all competitions this season enable fifth-placed Tottenham to close the gap on Manchester United, in fourth, to three points.
Conte's team had conceded 21 goals in their previous 10 league matches.
"I was just trying to get myself into a position where I can get half a yard. I used the defender to bend it around him. It was a nice goal," Kane said.
"I have been playing football long enough now to know where the goal is. It is just instinct."
While Kane rightly took the spotlight, Conte was just as pleased his players answered his pre-match rallying cry to show more resilience in defence.
"It was a big win. I had a good answer from my players. I asked them for solidity of the last season and the will and desire to fight and to be resilient," Conte said.