Mexico needed a spectacular Raul Jimenez goal in the 85th minute to beat Panama 2-1 on Friday and revive its hopes of qualifying for the World Cup.
"What a spectacular goal, really beautiful and above all very emotional," Victor Manuel Vucetich said after his first match as Mexico's coach.
The result moved Mexico into fourth place in CONCACAF qualifying, three points ahead of Panama and three points behind third-placed Honduras with one game to play.
The top three teams qualify automatically for the World Cup, while the fourth team faces an intercontinental playoff against New Zealand.
In the last round of games, Honduras is away to already-eliminated Jamaica and needs only a draw to secure a World Cup berth, while Mexico is away to Costa Rica and Panama hosts the United States. Both Costa Rica and the U.S. have already qualified for Brazil 2014.