Torres scored Atletico’s final penalty as they eliminated Bayer Leverkusen in a tense shootout to reach the Champions League quarter-finals in midweek and produced a towering header from Koke’s free-kick to get the hosts off to a perfect start after three minutes.
Tiago then nodded home from Raul Jimenez’s flick-on a minute before half-time to lift Atletico to just six points behind leaders Barcelona.
The top two in La Liga go head-to-head on Sunday as Barca host Real Madrid at the Camp Nou.
After 120 gruelling minutes against Leverkusen on Tuesday, Atletico boss Diego Simeone was without the injured Miguel Angel Moya, Mario Mandzukic and Raul Garcia, as well as Miranda through suspension as he made six changes in all.
However, the feel good factor around the Calderon continued when Torres rose highest to loop home a wonderful header for his fourth goal since returning to Atletico in January.
The hosts were desperately unlucky not to be 2-0 up inside the first 10 minutes when Koke’s thunderous shot came off the inside of the post and somehow didn’t rebound into the net after hitting goalkeeper Vicente Guaita on the back.
Mexican striker Jimenez had been given his first league start since September by Simeone and made his presence felt as he pulled a shot just wide and then nodded down a cross for Koke, which the Spanish international could only turn into the hands of Guaita.
Getafe’s only clear chance of the afternoon came on 25 minutes when Fredy Hinestroza found space inside the box, but his effort was amazingly blocked by Jose Maria Gimenez diving head first to divert the ball from danger whilst he was lying on the ground.
Only a brilliant goal line clearance from Mehdi Lacen denied Jimenez a goal as Atletico continued to threaten from set-pieces.
And the champions did finally extend their lead when Koke’s free-kick was flicked-on by Jimenez and Tiago timed his run to head home unmarked at the back post.