After a flurry of chances for the home side, Suárez leveled from close range in the 63rd minute and then headed the winner in the 74th, giving the European champions the edge before next week’s second leg at the Vicente Calderon.
Atlético got off to the ideal start when Torres fired Koke’s pass through the legs of keeper Marc-Andre ter Stegen after 25 minutes but 10 minutes later he was dismissed for a second booking as they suffered a seventh straight loss to Barca.
Atlético had been in confident mood after thrashing Real Betis 5-1 in la Liga on Saturday and were looking to take advantage of Barcelona, who were reeling from a 2-1 home defeat by Real Madrid that ended their record 39-game unbeaten run.
Simeone’s men defended as a team and their organised play and high pressing interrupted Barca’s usual quick passing game.
After Lionel Messi and Neymar missed the target in the early stages, Atlético pounced with their first proper chance.
After a long spell of possession, Koke received a pass from Gabi and took a touch before threading the ball into the path of Torres, who got his 11th goal in 15 matches against Barcelona.
The former Liverpool and Chelsea striker received his first booking for a late tackle on Neymar in the middle of the pitch four minutes after scoring and got his marching orders for a second yellow minutes later for fouling Sergio Busquets.
Diego Simeone’s side had two sent off when they lost to the Catalans in La Liga and were again punished for indiscipline.
After the break Messi was inches away from his 500th career goal with a scissors kick before Neymar hit the far post and then sent a shot whistling just wide.
Barcelona broke Atletico’s resistance when Suárez diverted Jordi Alba’s low cross home with his shin and then powered into the area to head Dani Alves’ cross past Jan Oblak to score the winner with his eighth Champions League goal this season.