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 rallied in the second half.
Suarez netted a brace to put Luis Enrique’s side in charge of the tie ahead of the second leg on April 13.
It had been a positive start by the home side.
Lionel Messi sent a left-foot volley wide before Neymar headed over a floated cross from the right by full-back Dani Alves.
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 in.
Torres then went into the notebook for a foul on Neymar and the Spaniard was sent off after German referee Felix Brych showed him a second yellow card for going through the back of Busquets.
Following the restart, the home side took control as Atletico were pressed back into the own half.
The pressure eventually told as Suarez equalised on 63 minutes, bundling the ball in from close range.
There was, however, nothing scruffy about the forward’s second goal of the night, which came on 74 minutes as he headed in Alves’ cross.
ter Stegen, Dani Alves, Pique, Mascherano, Jordi Alba, Rakitic (Rafinha 64), Busquets (Sergi Roberto 81), Iniesta (Turan 83), Messi, Suarez, Neymar.
Oblak, Juanfran, Lucas, Godin, Filipe Luis, Koke, Gabi, Saul (Correa 90), Griezmann (Thomas 75), Carrasco (Fernandez 53), Fernando Torres.
Felix Brych (Germany).