The Super Cup winners, who have been struggling in La Liga, left former Monaco man Thomas Lemar on the bench as they aimed to get their season back on track.
But against the run of play, Leonardo Jardim’s side took the lead after a mistake from Saul Ñíguez was pounced on by Radamel Falcao’s whose low cross was eventually prodded in by Samuel Grandsir.
1’ – DISALLOWED GOAL: The ball is hammered in from two yards by Godin but Gimenez is pulled up for a foul in the buildup following a free-kick which was played short.
6’ – COSTA CHANCE! Griezmann drops deep and dinks the ball over the top for Costa who flashes a shot in but the keeper appeared to get a finger to it.
18’ – GOAL FOR MONACO! Grandsir prods the ball in from close range after Falcao pounced on Saul’s mistake to put in a low cross.
31’ – GOAL FOR ATLETICO! Costa is through on goal and rifles the ball in from Griezmann first time.
45’+1 – GOAL FOR ATLETICO! Gimenez with a bullet header from Koke’s corner, the keeper got a hand to it but couldnt keep it out.
50’ – DISALLOWED GOAL: Costa fires the ball into the bottom corner but he is off-side although he is claiming the last touch was from a Monaco player.
90’+1 CLOSE! – Glik with a header at the back post which goes inches wide under pressure from Juanfran.
Diego Simeone’s side eventually found their rhythm and hit back when Antoine Griezmann, playing in a deeper role, pulled off a deft through ball for Costa to fire the ball into the net.
And the visitors took the lead in first half stoppage time through Jose Gimenez’s bullet header from Koke’s corner.
The French side, missing Danijel Subasic, Aleksandr Golovin, Rony Lopes, Stevan Jovetic, Willem Geubbels and Pietro Pellegri, were guilty of a string of poor crosses in the final third after the break.
Adama Traore, Moussa Sylha and Jordi Mboula came on as they switched to a 4-4-2 to match the Spanish side but they were unable to find the net.
And Atletico, who brought on Lemar who got a warm welcome from the home fans, held on for the win to go joint top of the group.