Striker Francisco Fonseca and defender Joel Huiqui scored in each half before a 25000 crowd at the Chasefield stadium in Phoenix Arizona against opponents who played almost the entire game with 10 men.
Mexico gave four players -- goalkeeper Guillermo Ochoa defender Antonio Olvera midfielder Andres Guardado and striker Alonso Sandoval -- their international debuts as they tried to break their duck against European opposition under coach Ricardo La Volpe.
Mexico one of the eight seeded nations at next year's World Cup had previously lost to Germany and Bulgaria and drawn with Greece Poland Sweden and Iceland during La Volpe's reign which began after the 2002 World Cup.
Their last win against a European side was against Croatia during the 2002 finals.
Suarez three days short of his 37th birthday started the game and played 69 minutes as he equalled the record of Saudi Arabia goalkeeper Mohamed Al-Deayea.
The game swung Mexico's way in the 10th minute when Hungary had Denes Rosa sent off for an ugly challenge on Olvera.
Fonseca opened the scoring in the 32nd minute heading home from close range for his 15th goal in 23 internationals since his debut last year.
Huiqui added the second six minutes after halftime when he fired home from six metres following a free kick on the left for his first international goal.