The Spain striker opened the scoring with a header after just three minutes of play and his Portuguese team-mate nodded home a second just before half-time
The Spain striker netted Atletico's decisive penalty in the Champions League shoot-out 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.
Simeone made the surprising decision to omit birthday boy Antoine Griezmann from his starting XI, with Raul Jimenez and Torres – who had just one Liga goal between them this season prior to kick-off – leading the line instead.
Nevertheless, Atletico began the contest positively and Simeone's selection was vindicated after only three minutes, as Torres met Koke's free-kick with an emphatic header to find the top-left corner.
Getafe were being overrun and were lucky to avoid falling further behind six minutes later, as Koke's low drive came back off the right-hand upright, hit goalkeeper Vicente Guaita and then struck the other post.
Koke missed an even better chance when blasting straight at Guaita from point-blank range in the 19th minute and Getafe could have capitalised a few moments later had it not been for some incredibly brave defending by Jose Maria Gimenez.
The Uruguayan dived head first at the feet of Fredy Hinestroza 10 yards from his own goal, denying the Colombian an almost-certain equaliser.
But Atletico continued to dictate proceedings and eventually netted a second just before the break, as Tiago latched on to Jimenez's flick-on and headed in at the back post.
Getafe made a slight improvement after the break, although Atletico remained in the ascendancy initially and almost added a third in the 56th minute, only for Diego Godin to head Koke's corner just wide of the target.
Atletico appeared content to sit back and invite pressure on to themselves as the second period progressed and, while Getafe did see more of the ball, Jan Oblak was rarely troubled in the hosts' goal.
The 64th-minute introduction of Griezmann saw Atletico's control return and Torres almost doubled his tally 13 minutes from time, but his diving header from Juanfran's delivery went just wide and the hosts settled for a two-goal triumph.