All the second-half spot-kicks were awarded for handball at the Vicente Calderon stadium, the first two resulting in dismissals for Sevilla defender Emir Spahic and Atletico's Diego Godin.
Diego Costa, leading the line in the absence of the injured Radamel Falcao, put Atletico in front after Spahic was given a second yellow card for falling on the ball and striking it with his arm in the 48th minute.
Godin was shown a straight red seven minutes later when Alvaro Negredo's goal-bound effort brushed his arm. Negredo then equalised from the spot, the first goal Atletico have conceded at home in more than 1,000 minutes of play.
Costa converted his second penalty in the 71st minute after Sevilla full-back Fernando Navarro tumbled to the ground and handled.
Navarro was also sent off five minutes from time for bringing down Costa when he was through on goal.
"The job of taking the two penalties fell to me and it's great I scored them but the important thing was to win the game," Costa said in an interview with Spanish television broadcaster Telecinco.
"We were very superior and we had a lot of chances to score more," added the Brazilian.
Holders Barcelona and 2011 winners Real Madrid drew their first leg 1-1 at the Bernabeu on Wednesday.
The game between Atletico and Sevilla was a repeat of the 2010 final, which was won 2-0 by the Andalusians.
"It was a shame about the second sending off because we had to accept the result and hang on for the second leg," Sevilla coach Unai Emery told a post-match news conference.
"We knew that Atletico are having a great season and we would have to be very focused to get a good result," he added.
"It was a very tough match, very demanding."
Barca host Real and Atletico visit Sevilla in the second legs at the end of February with a place in May's final at stake.