Suarez converting a through ball from Philippe Coutinho which split the Valencian defence.
Barca showed few signs of lost confidence early on and after 15 minutes they took the lead, Coutinho drifting in from the right and, after spotting Suarez's angled run, poking a superb pass in behind.
Heavy rain and Wednesday's defeat in Italy limited the attendance to 69,544, 16,000 less than Camp Nou's last daytime home game a month ago, but despite the flat atmosphere, the fans' efforts to attend were rewarded by an entertaining game.
The Spanish champions-elect will also be consoled by the thought that their bitter rivals Real Madrid are now languishing in fourth place in La Liga.
The Barca coach praised his players for putting the Roma defeat behind them but said their European exit had punctured their enthusiasm for the unbeaten record. Soler played in Rodrigo Moreno but Ter Stegen made up for his mistake by pushing the shot onto the bar.
Barca were two up six minutes after the restart when Samuel Umtiti beat Gabriel Paulista to head a Coutinho corner down past Neto in the visitors' goal. "The public can be angry about the Champions League, like us, but this is a recognition of the great season we are having in the league, which now seems to have been forgotten".
On the not-so-bright side, Valencia entered the weekend one point ahead of Real Madrid for third place, thus beating Los Che opened the door for Los Blancos to return to third on Sunday.
Suarez, who opened the scoring before Samuel Umtiti's header sealed the win, says the reaction from some of the press and the fans makes it feel as though winning the domestic title nearly does not matter.
"Even though I couldn't play in the Champions League, I still wanted us to win it. We wanted to reach the final".
'We know we failed the other day but we have important things to win this season'. This is the most important thing.