Diego Costa scored a valuable away goal, to add to last week's 2-0 victory at the Calderon, after a dreadful misunderstanding in the Betis defence just before halftime.
Chasing a long punt over the top Betis defender Antonio Amaya did not see his keeper Casto Espinosa had raced out of the area and he headed the ball past him allowing Costa to run through and tap into an empty net.
La Liga's second-placed side Atletico successfully stifled their hosts until they gave away a penalty in the final minute to concede their first goal in six games in this season's cup competition.
Atletico defender Diego Godin bundled over Jorge Molina in the area and the striker netted from the spot.
Atletico set up a last-four clash with Sevilla, who beat them 2-0 in the 2010 Cup final. Sevilla swept aside Real Zaragoza 4-0 on aggregate in their quarter final.
On the other side of the draw, Real Madrid beat Valencia 3-1 on aggregate, despite having two players sent off in Wednesday's 1-1 second-leg draw at the Mestalla.