Barca scored six in the second half - Ivan Rakitic fired in, before Suarez slid in for his hat-trick and then tapped in Neymar's selfless pass.
Messi rolled in, then Marc Bartra's solo goal and Neymar's simple finish from close range sealed the rout.
Barca had let a nine-point lead at the top of La Liga slip but victory on Wednesday was never in doubt from the moment Suarez scored his 46th goal of the season from a corner.
Suarez took his tally to 49 before the end of the night and also contributed three assists as Barca were utterly dominant.
Wins for Atletico Madrid and Real Madrid mean that the title race remains tight. Barca are joined on 79 points by Atletico, with Real a point further back. There are four games remaining.
'We are not machines'
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"We are human, we aren't machines and we can all commit errors or have a bad game," Suarez told Spanish TV station Movistar+.
"This is a demonstration that the group is more united than ever and desperate to win the league. It is still in our hands."
Barca face Sporting Gijon, Real Betis, Espanyol and Granada in their final games.
"It was a spectacular result for us," said manager Luis Enrique.
"We have a wonderful challenge ahead of us to retain the league title. But there are still four games to go and I'm sure it's not going to be easy."