Betis had won their previous five home games across all competitions and Abde Ezzalzouli almost gave them the perfect start inside six minutes as the winger controlled a crossfield pass on his chest and curled agonisingly wide of the far post from long range.
Instead, it was Atletico who drew first blood, when captain Koke whipped a 12th-minute corner to the near post and David Hancko nodded home his second goal of the season.
The visitors should have doubled the lead four minutes later when deadline day signing Ademola Lookman burst through one-on-one, but the debutant dragged his shot wide.
Nelson Deossa spurned the chance to score his first Betis goal when he fired wide from the edge of the area midway through the half, and moments later that miss was punished.
Giuliano Simeone scored in Atletico’s 2-0 LaLiga victory here in October and was on target again on his return to Estadio La Cartuja, as he tapped home Matteo Ruggeri’s cutback after Los Rojiblancos scythed the hosts open down their left side.
Lookman opened his account for Atletico eight minutes before half-time too, shifting Pablo Barrios’ pass on to his right foot, cutting inside two defenders and squeezing a shot past Adrian to finish a lightning counter-attack.
Betis had failed to score in just one of their previous 29 Copa del Rey games, and Ezzalzouli could have pulled a goal back three minutes after the restart, only to scuff his shot straight at Juan Musso.
Atleti continued to threaten, though, and they scored their fourth just after the hour mark when Lookman found the onrushing Antoine Griezmann, who fired through the hands of Adrian to score his fourth Copa del Rey goal of the season.
With their place in the last four secured, boss Diego Simeone rang the changes and one of the substitutes, Thiago Almada, tucked home his fourth of the season across all competitions seven minutes from time, after Adrian saved Griezmann’s initial effort.
That put the seal on an 11th win in the last 14 H2Hs for the 10-time champions, inflicting only a fourth home defeat of the season across all competitions on Betis in the process.
The hosts won’t want to see Atletico again for a while but the fixture gods haven’t been kind to Manuel Pellegrini’s side, who now face a trip to their cup conquerors in LaLiga on Sunday.
Flashscore Man of the Match: Ademola Lookman (Atletico Madrid)