An own goal by Cruz Azul striker Emanuel Villa as he tried to clear a corner put home side Monterrey in front after only three minutes of Thursday's match in the northern city of Monterrey.
However, Paraguayan Cristian Riveros scored with two headers in the next 15 minutes to put Cruz Azul ahead and Villa increased their lead past the half hour when he netted a loose ball in the box for his league-leading 19th goal.
Monterrey wrested control from the visitors in the second half and Chile striker Humberto Suazo reduced the arrears two minutes after the interval.
Sergio Santana equalised with a header from a cross by Paraguayan Osvaldo Martinez with 19 minutes to go.
Suazo struck the winner in the dying minutes when he poked the ball home after it was spilt by visiting keeper Jesus Corona under pressure from Martinez.
"The players know that what they did is manly, with a lot of temperament and character," Monterrey coach Victor Vucetich said.
"It was an extraordinary recovery by the squad and I must congratulate them for that, for their great desire to overcome (the odds)," he told reporters.
"Monterrey did enough to deserve the victory," conceded Cruz Azul coach Enrique Meza. "We lost the ball and there isn't a team that can withstand that.
"We know we made mistakes but there are three days to go to the decisive match because this result isn't definitive."
San Luis, eliminated in the quarter-finals two weeks ago, sacked Argentine coach Miguel Angel Lopez and replaced him with Ignacio Ambriz.
Ambriz, 44, was assistant to present Mexico coach Javier Aguirre when he was in charge of Spanish teams Osasuna and Atletico Madrid. He was also Aguirre's right-hand man with the Mexico team at the 2002 World Cup.
