In the first leg round of 16 tie, the Peruvian side opened the scoring after 80 minutes when Pablo Vitti started a counter-attack and Andy Polo crossed the ball into the box.
Raul Ruidiaz finished the move to cheer the away fans in the Estadio Mundialista.
However, Gonzalo Cabrera equalised with only two minutes remaining.
Universitario's goal might be crucial in the second leg to be played on October 20 in Lima.
Polo told Fox Sports: "It's a pity that we failed to take profit from that goal. We came here to win the match, but a draw is not bad at all.
"There are 90 minutes left and we'll play them as a final."
The 2007 Copa Sudamericana champions Arsenal of Argentina secured a goalless draw away to Paraguay's Olimpia in the first leg match.
Arsenal have a good chance to make it into the quarter-finals in the second leg, to be played on October 19 in Argentina.
Arsenal keeper Cristian Campestrini was satisfied with the point at the Estadio Defensores del Chaco in Asuncion.
He said: "These are 180-minute finals and they were a very tough pitch and rivals tonight [Thursday].
"This is a positive result, but we have gained nothing yet."
In Rio de Janeiro, Colombia's Santa Fe obtained a 1-1 draw away to Botafogo of Brazil.
Santa Fe took an early lead thanks to an eighth-minute goal by Omar Perez, following good work by Alejandro Bernal.
However, Caio equalised 20 minutes after the break.
The second leg will be played on October 25 in Bogota.