Fernando Torres – who scored the final penalty against the Germans – opened the scoring in the third minute following a free-kick and Tiago doubled the advantage just before half-time, also converting from a set-piece.
That was Atletico’s first league win in four matches following three successive draws and keeps them one point behind third-placed Valencia, while Getafe slumped to a third defeat in four matches under interim coach Pablo Franco and are just four points above the relegation zone.
Malaga’s bid for a top-six finish suffered a blow as they suffered a second successive away defeat, going down 1-0 to a Gael Kakuta first-half header at Rayo Vallecano.
That was Rayo’s fourth successive Primera Division home win and was made easier by the 74th-minute dismissal of Malaga defender Marcos Angeleri following a second booking.
Malaga’s defeat allowed in-form Athletic Bilbao to move to within five points of them as the Basque side defeated Almeria 2-1 at San Mames.
Athletic have been the form team in La Liga over the last few weeks and Saturday’s win, secured by goals from Xabier Etxeitia and Mikel Rico in the opening half-hour, was their fifth on the trot.
Almeria did manage to reduce the deficit when home defender Mikel Balenziaga put through his own net at the start of the second half, but they never really threatened an equaliser as their winless run stretched to six games.
Celta Vigo are up to ninth after earning a deserved 1-0 win at Levante, although they left it late with substitute Charles Dias netting the winner three minutes from time.
Levante remain in trouble near the foot of the table, along with Granada and Eibar who shared a goalless draw on Saturday.
That result saw Eibar end a run of eight successive defeats but they are still just three points clear of the bottom three, while Granada remain in 19th after failing to make their dominance count at the Estadio Nuevo Los Carmenes.