A Rafael Olarra header a couple of minutes after the interval meant a big result for Gerardo Pelusso's side courtesy of an away goal which might prove crucial in the second leg. Universidad were solid in the first half, their defence not allowing Guadalajara near to goalkeeper Miguel Angel Pinto.
In the 47th minute, Argentinian playmaker Walter Montillo sent a free-kick into the area and Guadalajara defender Hector Reynoso's clearing header only reached Juan Manuel Olivera. He headed the ball on to Olarra, who duly nodded the ball into the net.
However, Omar Arellano equalised five minutes later after Pinto parried an Omar Bravo header from Alberto Medina's corner. Olarra warned his team-mates to take nothing for granted as they seek a first Copa Libertadores final appearance.
"Only the first half is over," he told Fox Sports. "They are great opponents with technique and talent. We should not be over-confident.
"We played a great match as visitors and we are very confident. We have to go step by step. We are now focused on the second leg and I think this team has what it takes."
The second leg will be played next Tuesday at the Estadio Nacional in Santiago. In the other semi-final tie, Brazilian sides Internacional and Sao Paulo meet in Porto Alegre on Wednesday night.