Bellingham opened the scoring with a volley in the 62nd minute at a rain-soaked New York New Jersey Stadium before turning provider, delivering the cross that Kane converted to secure top spot in Group L.
Kane's strike was his 11th World Cup goal for England, taking him past Gary Lineker as the nation's leading scorer in the competition's history - a record that has stood for 36 years.
The England captain has now scored three goals at this tournament, adding to the six he scored at the 2018 World Cup in Russia and the two he scored in Qatar in 2022. Lineker won the Golden Boot with six goals at Mexico 1986 before adding four more at Italia 1990.
Speaking after the match, Bellingham was full of praise for the Bayern striker.
"I think I've built a good relationship with Harry over the last four or five years, especially after Qatar and I playing so close together, and it's an honor to play with him," the midfielder told reporters.
"He's the best England player of all time. He's the one who showed up more than anyone, more than any England player. And so it's quite easy to play with him.
"In all honesty, he's at a level at the minute that's just incredible. You don't doubt him at all in terms of whether he's involved, whether he's not. You know, he's gonna make a difference in the game, and he did it again today."
England's victory means they will face DR Congo in the Round of 32, but Bellingham insisted the identity of their opponents is of little importance.
"It can't matter really," he said.
"We have to go through all the best teams, all the teams that deserve to be in the next round.
"We have to try and go through them as if they're if they're the same thing. We respect 100 per cent whoever we play against, but we also have to be aware that to win the World Cup you're gonna have to play against tough teams."
Kane was replaced in the 84th minute by Jordan Henderson, who became the first player for England to compete at four World Cups. But the Brentford midfielder said the day belonged to his teammate.
"Seems with him he’s just continually smashing records everywhere he goes, and (he has) scored so many goals," Henderson said.
"He's been an incredible player so far for England, and continues. He's still got a long way to go, but yeah, he deserves everything he gets.
"He's been an incredible player, incredible teammate, and (I am) delighted for him to be able to get that record."