Jude Bellingham scored two goals 98 seconds apart on Sunday night (Monday AEST), Harry Kane converted a penalty when England were down to 10 men, and the Three Lions hung on to end the co-hosts tournament.
England move on to face Norway on Saturday in Miami Gardens, Florida, for a spot in the semi-finals.
Bellingham stunned the crowd of more than 80,000 at a venue where Mexico were 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.
Julian Quinones scored for El Tri in the 42nd minute, and the game appeared to turn in Mexico's favour when England's Jarell Quansah was sent off in the 54th for a dangerous foul on Jesus Gallardo.
Australian referee Alireza Faghani remained a busy man, and 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 has six goals in this tournament, 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.
Mexico attacked relentlessly over the final 21 minutes, plus 11 minutes of stoppage time, but goalkeeper Jordan Pickford and England's defenders held steady.
Mexico have not reached the quarter-finals since hosting in 1986. Since then, they have lost in the round of 16 eight times, failed to advance past the group stage in 2022 and were disqualified from the 1990 tournament.
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