Torres fired Atletico ahead midway through the first half, but was then shown a second yellow card following a needless foul on Sergio Busquets.
Barcelona, who had seen their long unbeaten record ended following a late defeat at home by ten-man Real Madrid in El Clasico on Saturday, rallied in the second half.
Atletico went ahead on 24 minutes. Koke played a pass between the Barcelona defenders to find Torres in space at the edge of the penalty area, with the Spain forward showing great composure to slot the ball between the legs of goalkeeper Marc-Andre ter Stegen.
Torres then went into the notebook for a foul on Neymar and Atletico were reduced to ten men when Torres was sent off after German referee Felix Brych showed him a second yellow card for going through the back of Busquets on the half-way line with plenty of team-mates covering.
Following the restart, the home side took control and the pressure eventually told as Suarez equalised on 63 minutes, bundling the ball in from close range. There was nothing scruffy about the forward’s second goal of the night, which came on 74 minutes as he headed in Alves’ cross.