The hosts got off to a flying start as Pedro Rodriguez, once again deputising for Neymar, opened the scoring with a smart finish from Ivan Rakitic's wonderful through ball inside two minutes yesterday.
Barca then struggled to build on their lead for the rest of the first period, but Suarez capped another quick start to the second period when he poked home from close range to end a seven-game drought in the league since returning from a four-month ban for biting.
"I was able to score and that helps relax me. I don't know if we were affected, but the draw with Getafe last week annoyed us. We had to come here today and show that we're in the fight for the Liga title," Suarez said.
"Scoring is always important, but with the support of everyone we all knew that this happy moment would come. I'm a forward and I have to score goals, but I'm also helping the side to achieve its aims.
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Pedro was rewarded for his hat-trick in the 8-1 thrashing of Huesca in midweek with a start as Neymar was only fit enough for the bench.
The Canary Islander continued his scoring streak when he latched onto Ivan Rakitic's intelligent left-footed ball over the top and lashed the ball into the roof of the net to register his sixth goal in as many games.
Suarez was inches away from making his mark with an acrobatic effort that flew into the side-netting before Juan Carlos did well to tip a header from Pique over the bar.