The midfielder opened the scoring just after Braian Rodriguez's red card, while the forward netted just eight minutes later to secure three precious points for Diego Simeone's menAtletico Madrid heaped the pressure on rivals Real Madrid ahead of the Clasico with a 2-0 win at 10-man Real Betis on Sunday.
The Rojiblancos, who hold the edge on their city rivals because of their superior head-to-head record, moved level on points with their neighbours at the top of the Liga table after second-half strikes from Gabi and Diego Costa gave them their 10th away win of the 2013-14 season.
If Atletico and Real end the campaign on the same number of points, Diego Simeone's side will finish higher because of their win and draw garnered from the two derby meetings this term.
They were made to work for their latest victory, but eventually their quality shone through against bottom-placed Betis, just two hours before Madrid's much-anticipated clash with third-placed Barcelona at the Santiago Bernabeu.
Costa had a goal ruled out for offside in the first half, a decision that appeared to be harsh, but the match swung in Atleti's favour when Braian Rodriguez was sent off for a second yellow card in the 56th minute.
Gabi capitalised with a stunning 25-yard strike just two minutes later and Costa then showed his predatory instincts with a clever left-foot finish just after the hour, as struggling Betis' slim chances of survival took another blow.
The hosts started quickly as lone striker Jorge Molina and Juan Carlos had long-range attempts on goal, and, initially at least, they kept Atletico quiet.
Arda Turan was the main outlet for the visitors and he showed his class when he got to the byline, beat three and crossed for Costa in the 23rd minute, but Javi Chica nodded his delivery behind for a corner.
The first half's main talking point almost immediately followed, as an unlucky Costa had a goal cancelled out.
The forward reacted quickly to a flick-on header, taking a touch and smashing a left-foot volley into the roof of the net despite the best efforts of defender Antonio Amaya, only to see the offside flag raised.
Replays suggested the decision was incorrect and tempers began to fray as Braian and Filipe Luis were booked, while Costa and Paulao clashed more than once.
Costa was denied twice by good Betis defending before the interval but the hosts - perhaps fatigued after their Europa League last-16 loss to city rivals Sevilla on penalties on Thursday - faded in the second half.
Just after Braian was given his marching orders, Gabi produced his moment of genuine quality, hitting the bottom right corner of the net with an incredible shot that gave Adan no chance.
Raul Garcia then missed a sitter, after Costa's lay-off, and was immediately substituted, but his strike partner netted a second, reacting to Koke's flick-on header with a fine finish for his 23rd Liga goal of the season.
Costa could have had another, only for his header to hit substitute David Villa in an offside position, but two goals were more than enough for the title challengers as the game petered out in the final stages.