The Catalan giants lead Atletico Madrid solely thanks to their superior head-to-head record with Real Madrid just one point back in third with four games to go.
However, having taken just one point from their previous four league matches, Suarez believes Barca are fully back on course for a 24th La Liga title.
"We needed that victory. We came off the back of many games suffering and, as we are human, the defeats hurt," he said.
"We are the leaders and we are convinced we are going to win it. We aren't contemplating anything other than winning."
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Lionel Messi and Neymar were also on target against Deportivo as Barca's star front three responded in style to their critics as fatigue appeared to catch up with the South American trio in the past month after a hugely demanding season as Barca competed in six competitions.
And Suarez reserved special words of support for Neymar, whose performances and off-field attitude had been the target for particular criticism during Barca's slump.