Despite a host of star names returning after being rested for the Copa del Rey semi-final second leg, Barca were flat early on against a Celta side missing suspended strikers Iago Aspas and Fabian Orellana as well as the injured Nolito.
Celta were handed an early scare when Messi curled a free-kick marginally wide 11 minutes in while Neymar was denied from point blank by Sergio as Barca grew into the game.
Sergio’s opposite number Claudio Bravo got down smartly to his left to save Carlos Plana’s effort but the former Barca man then conceded the free-kick that led to Messi’s opener.
After a foul on Suarez, Messi sent his superb dead-ball effort into the top right-hand corner beyond a helpless Sergio.
However, Alba clumsily clipped Guidetti in the area seven minutes before half-time, allowing the Sweden international to restore parity with an emphatic equaliser down to Bravo’s right.
Messi almost restored Barca’s lead within two minutes of the restart when he angled an effort onto the post following an impressive virtuoso run and pass from Neymar.
The hosts were back in front through Suarez thanks to a trademark moment of Barca brilliance, as the Uruguayan controlled Messi’s perfect chipped pass and slotted home on the half-volley.
Having ended a spirited Celta stand, Barca’s attacking trident all had a hand in the third goal, with Messi finding Neymar, whose effort from a difficult angle rolled toward the line before being stabbed home by Suarez.
But Messi wowed the Camp Nou once more when, having been brought down by Jonny, he laid his penalty off for Suarez to finish amid a remarkable final half-hour that saw Rakitic join the party with a fine lobbed finish.
A deserved goal for Neymar in the 90th minute capped a hugely impressive attacking display from the champions, who made it six successive league wins in style against a shellshocked Celta.