Libertadores: Guadalajara sneak through despite defeat
The Argentine side, South American champions in 1994, took an early lead when Uruguayan striker Santiago Silva sent a glancing header inside the far post from a Maxi Moralez cross from the left in the third minute.
Velez had the Mexicans against the ropes towards the end and substitute Rolando Zarate out-jumped keeper Liborio Sanchez to head their second from close range in the final minute, setting up a dramatic four minutes of stoppage time.
"The team was pure heart in the second half but we couldn't win," Zarate told Fox Sports.
Champions of the Argentine Clausura in the second half of last season, Velez were left empty-handed having put all their efforts into the tournament and dropped points in the league this year after fielding a reserve side in several matches to rest the first team.
The damage had been done in Guadalajara where the "Chivas", who move into a quarter-final tie with Once Caldas of Colombia or Paraguay's Libertad, won the first leg 3-0 last week.
Three-times winners Sao Paulo made heavy weather of their tie with Peruvian champions Universitario, taking it 3-1 on penalties after finishing 0-0 on aggregate. They hit the bar once in each half.
Universitario goalkeeper Luis Llontop, who had kept his team in the game with some good saves, also gave them a head start in the shootout by saving Sao Paulo's first spot kick taken by keeper and captain Rogerio Ceni.
However, once ahead the Peruvians lost their nerve and took poor penalties, with Ceni saving two and the other going wide as Sao Paulo progressed to a quarter-final tie against fellow Brazilians Cruzeiro or Nacional of Uruguay.