The Uruguay striker robbed defender Francisco Noguerol in the 26th minute and after sprinting clear lashed a powerful shot into the bottom corner past goalkeeper Yoel Rodriguez.
Celta, relegated at the end of the 2006/07 season and 17th out of 22 in the second-tier standings, battled valiantly in front of their vociferous fans and almost snatched an equaliser in the 84th minute.
The impressive Roberto Trashorras cut in from the left and Jose Luis Mato headed the midfielder's cross against the bar.
Atletico will play Racing Santander in next month's two-legged semi-finals after the Cantabrians won 3-0 at Osasuna on Wednesday for a 5-1 aggregate victory.
Getafe squeezed through to the last four on away goals earlier on Thursday after a 2-2 aggregate draw against La Liga rivals Real Mallorca and will play Sevilla in the semis.
Madrid-based Getafe, who lost to Sevilla in the final in 2007 and Valencia in the 2008 final, were beaten 1-0 in their near-empty Coliseum stadium but progressed thanks to a 2-1 success in the first leg.
Mallorca striker Aritz Aduriz, who earlier had a penalty saved, put the Balearic Islanders in front with a header in first-half added time.
Defender Ruben Gonzalez fluffed a golden chance to double the visitors' lead five minutes after the break, heading over from close range.
Sevilla, conquerors of holders Barcelona in the last round, lost their quarter-final second leg 1-0 at home to Deportivo La Coruna on Wednesday but went through 3-1 on aggregate.
