In an early Sunday kick-off, Diego Simeone's side were fired to victory by all-South American trio Eduardo Salvio, Diego and Radamel Falcao.
They move up to seventh, five points behind fourth-placed Malaga.
Argentine winger Salvio combined with another South American, Brazilian left-back Filipe Luis, to loop a fine header in midway through the first half.
In his first start for nearly two months, Brazilian playmaker Diego doubled Los Rojiblancos’ lead just after the hour mark with a tap-in after his initial header hit the bar and rebounded into his path.
Colombia striker Falcao - who had set up Diego’s goal - completed the win on 77 minutes with a cool finish from Juanfran’s cross.
The former Porto forward had earlier seen an inventive finish ruled out for offside.
Atletico now have 42 points, five behind Valencia and Malaga, in third and fourth respectively.
Getafe slip to 10th, having been level on points with Atletico before the match.