Coach Gregorio Manzano rested most of his first-choice players at Albacete's Carlos Belmonte stadium and the fired-up home side took the lead from the penalty spot in the 31st minute after the referee ruled Alvaro Dominguez had handled the ball.
Atletico had a chance to level five minutes into the second half when Juanfran was felled in the area by Albacete captain Miguel Nunez Borreguero, who was shown a straight red card.
Spain Under-21 international Adrian sent his spot-kick over the crossbar and Atletico's night took a turn for the worse 10 minutes later when Dominguez was dismissed for bringing down Albacete forward Antonio Sanchez de la Calle.
Home defender Zurdo whipped the resulting free-kick over the wall and into the corner of the net to make it 2-0 before Adrian made the most of a defensive howler to pull a goal back 20 minutes from time.
Albacete, who have had a couple of stints in Spain's top flight, have a famous majority shareholder in local hero Andres Iniesta and their shirts carry the name of the Barcelona and Spain playmaker's family wine business.
The Manchegan club will attempt to preserve their lead when they visit the Spanish capital for the second leg at the end of the month.
Atletico coach Manzano said he accepted Thursday's result and was confident the team could turn the tie around at their Calderon stadium.
"Clearly because of the difference in divisions, Atleti were the favourites but Albacete began with more intensity," Manzano told a news conference.
Atletico's La Liga rivals Athletic Bilbao had a relatively easy night at third-tier Real Oviedo in Thursday's later kick-off, winning 1-0 thanks to an 11th-minute strike from forward Oscar de Marcos, who also hit the post late on.
The remaining last-32, first-leg matches are next week.
