In the same stadium where England fell victim to Diego Maradona's Hand of God goal in the 1986 World Cup against Argentina, it was the foot of Kane that gave the nation redemption 40 years later.
Bellingham scored two goals 98 seconds apart in the first half on Sunday night (local time).
Some six minutes after Jarell Quansah was sent off, Kane converted a penalty to restore England's two-goal lead.
Mexico attacked relentlessly over the final 21 minutes, plus 11 minutes of stoppage time.
But goalkeeper Jordan Pickford and England's defenders held steady in a chaotic end to the game refereed by Australian Alireza Faghani.
England move on to face Norway on Saturday in Miami Gardens, Florida, for a spot in the semi-finals.
"It was a crazy game. We had to fight," Kane said, his voice hoarse.
"I can't really talk, but the occasion, the team, everything against us, we found a way.
Bellingham stunned the crowd of 80,824 at a venue where Mexico was unbeaten in 10 World Cup matches, including three this year, when he scored on a header in the 36th minute and again in the 38th on a pass from Kane.
Bellingham told England fans to have the day off work and school to celebrate the famous World Cup win, with a thunderstorm meaning kick-off was delayed until 2am (UK time).
"Text your bosses and tell them you're not coming in, simple as that," he said.
"I have been an England fan since I was seven years old, the 2010 World Cup was my first one.
"I remember watching a few tournaments and seeing a few of the players that are now on TV talking about it ... it felt like the country never really got behind them.
"Kids stay off school, parents don't go to work, enjoy your day, have the day off if you can, these nights don't come often."
Julian Quinones scored for El Tri in the 42nd minute, and the game appeared to turn in Mexico's favor when Quansah was shown a red card in the 54th for a dangerous foul on Jesus Gallardo.
But England were awarded a penalty for a challenge by Mexico goalkeeper Raul Rangel, and Kane converted for his sixth goal of this tournament and 14th of his World Cup career, matching Gerd Muller of West Germany for fifth on the scoring list.
Kane sits one behind Lionel Messi, Kylian Mbappe and Erling Haaland in the Golden Boot race.
Kane then committed a foul that made him the first player since at least 1966 to score and concede a penalty in a World Cup game.
Raul Jimenez converted the kick with a stutter-step approach to move El Tri within 3-2.
"This is probably one of the biggest England wins in a while, probably the biggest one I can remember as a fan or player," Bellingham said.
"The best night of my England career."
Midfielder Jordan Henderson was taken to a hospital after the match with a wrist injury, coach Thomas Tuchel said.
He was hurt when he tumbled over an advertising board during the post-game celebration.
"It's quite a serious injury," Tuchel said.
