Ivan Rakitic, Lionel Messi, Marc Bartra and Neymar were also on target as Barca reasserted their control on the Spanish title race.
Victory moved Barca back three points ahead of Atletico Madrid and four clear of third-placed Real Madrid with both sides from the capital in action later on Wednesday against Athletic Bilbao and Villarreal respectively.
Barca had taken just one point from their last possible 12 in the league and been dumped out of the Champions League amidst a run of just one win in six games that threatened to derail their season.
However, they remain in control of their own fate and few would bet against them winning their last four games and claiming a 24th Liga title after a performance as good as any in the 39-game unbeaten run they enjoyed prior to losing at home to Real Madrid earlier his month.
Suarez settled the visitors’ nerves after just 11 minutes when he outmuscled Sidnei to volley home the opener despite the hosts’ desperate appeals for a foul.
Deportivo should have hit back immediately as Celso Borges shot meekly at Claudio Bravo with just the Chilean international to beat.
Borges then had an even better opportunity as he rounded Bravo, but Bartra got back to block his effort from point-blank range before Oriol Riera fired the follow-up over.
Suarez gave Barca the cushion they desired when he latched onto Messi’s sumptuous through ball to slot low past Manu.
The Uruguayan should have had a first-half hat-trick but he failed to turn home Alves’s fine cross from two yards out moments later.
Suarez made amends as he turned provider for Barca’s third just after the break when his cross to the back post was volleyed home emphatically by Rakitic.
Messi created the fourth with another defence splitting pass and Suarez kept his composure to seal his sixth hat-trick of a prolific season.
The relief amongst the Barca players was palpable as they seemed to click back into the form that had them set for a second consecutive treble before their sudden collapse in the previous six games.
Suarez was gifted his fourth of the night from Neymar’s unselfish cross despite Laure blocking his initial attempt on the line for his 49th goal of the season.
The former Liverpool striker then added a second assist to his four-goal haul as Barca again tore the Deportivo defence apart and his cut-back was gratefully tapped home by Messi.
Bartra joined the party as he galloped forward from his own half without facing a single strong Deportivo challenge before firing into the far corner.
And Neymar completed a perfect night for the Spanish champions when he tapped home at the far post from Suarez’s third assist of a spectacular display for his first goal in six games.