The Spain striker netted Atletico's decisive penalty in the UEFA Champions League shootout victory over Bayer Leverkusen on Tuesday and was integral again on Saturday, scoring the opener as Diego Simeone's men halted a run of three consecutive league draws.
It took the lively Torres just three minutes to put Atletico ahead against their local rivals, his first La Liga goal since May 2007 a fine header that delighted Simeone, who is reportedly closing in on signing a new contract.
Atletico dominated the first half at the Vicente Calderon and saw several fine chances go begging, Koke guilty of spurning two of those opportunities.
But Tiago opened up a deserved two-goal lead just before the break, with Getafe improving as a defensive unit after the interval.
Despite the visitors growing in stature in the second half, Atletico's advantage never looked in threat and victory sees the Champions League quarter-finalists close back to within a point of third-placed Valencia.
Athletic Bilbao made it five straight wins in all competitions with a hard-fought 2-1 victory at home to Almeria.
Xabier Etxeita headed Bilbao into a ninth-minute lead and Mikel Rico doubled it in the first half, lobbing a stranded Julian Cuesta from 25 yards.
Bilbao defender Mikel Balenziaga was unfortunate to score an own goal in the 47th minute, but his team held on as Almeria were reduced to 10 men late on when Fran Velez saw red.
The win sees Bilbao stay eighth, five points adrift of Malaga, who suffered their second loss in three games by going down 1-0 at Rayo Vallecano.
Levante remain in the relegation zone after conceding an 86th-minute goal to be beaten 1-0 at home to Celta de Vigo.
Relegation-threatened duo Granada and Eibar played out a 0-0 draw.
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