Luis Suarez and Lionel Messi scored twice in two minutes as Barcelona broke the resistance of 10-man Atletico Madrid on Saturday to go 11 points clear of their La Liga title rivals.
Diego Costa was sent off in the 28th minute at Camp Nou after insulting referee Gil Manzano but while Atletico held on for almost another hour, Suarez and Messi struck late to seal a pivotal 2-0 win.
The victory leaves Barca almost out of sight with seven games left to play and maintains momentum ahead of Wednesday's trip to Manchester United in the first leg of the Champions League quarterfinals.
"These three points were very important, we still have to finish the job but today's game was fundamental and could mean a lot," Valverde said. "We're very happy because we know exactly what Atletico are, an enormous team who scrapped until the end with 10 men. We were giving everything and Luis' goal was like a shot of adrenaline."
"Today we didn't just take one step, we took two steps forward, we obviously have a very big advantage now but there are still some games to go and it could still get difficult," Suarez told reporters. "This was another game which shows just how hard it is to win the league and we deserve a lot of credit for what we're achieving."
Costa's early dismissal left Atletico needing snookers just to avoid defeat, let alone pull off a win that coach Diego Simeone had said last week was the only result to keep their challenge alive.
"I asked the referee and he told me Costa said something to him," Simeone said. "Other players have said things and not been sent off but that does not justify what Costa did."
Suarez hit a superb long-range strike in the 85th minute, before Messi added a second in the 86th.