Suarez and Messi scored late goals to earn the Catalan club a crucial victory over Atleti.
Ernesto Valverde has agreed Barcelona are closing in on back-to-back LaLiga titles after beating Atletico Madrid 2-0 at the Camp Nou on Saturday.
Late goals from Luis Suarez and Lionel Messi handed Barca three points after Diego Costa's first-half sending off for dissent.
Atletico, who sit in second spot, are now 11 points adrift of the league leaders who travel to Manchester to take on Ole Gunnar Solskjaer’s Red Devils in the Champions League on Wednesday night.
And Valverde knows Barca are closing in as he said “it’s three important points” and “the work has to be finished” to prevent complacency setting in.
"It's three very important points," he told reporters as quoted by Marca. "We are closer to the title, but we still have it [to win].
"The work has to be finished. Today [Saturday] was a fundamental match because they can mean a lot.
"We are very happy because our opponent was second in the table and a huge team who has fought to the end with one less man."
Valverde hailed Suarez after the Uruguay international scored his seventh goal in nine matches across all competitions following a difficult spell.
"He [Suarez] always ends up being decisive," Valverde added. "He's a permanent headache for the opponents and you don't know when he's going to appear.
"He was fresh, with a spark, and he had a great goalkeeper [Jan Oblak] in front of him."