The Argentine bagged two with Philippe Coutinho, Gerard Pique and Ousmane Dembele all on the scoresheet to secure Barca’s place in the last-eight for the 12th year running.
Barca coach Ernesto Valverde dreaded repeating the fate of arch-enemies Real Madrid, who embarrassingly capitulated at the Bernabeu at the hands of Ajax last week.
The visitors suffered a further blow, losing keeper Anthony Lopes to a head injury in the first half, before conceding two early goals – although Lucas Tousart’s second-half volley spooked the Catalan giants.
Former Celtic striker Moussa Dembele squandered a brilliant chance to penalise the Catalans straight after as he fired the ball out wide, wasting Lyon’s dangerous counter-attack.
And it brutally came back to haunt Bruno Genesio’s men at the half-hour mark as Suarez easily lost Marcal’s marking with a turn only to set Coutinho up for a straightforward tap-in.
Lyon managed to pull one back courtesy of Tousart, who volleyed the ball in after a scramble in Marc-Andre ter Stegen’s box.
But Messi took matters into his own hands and inspired a flurry of late goals that saw him bag his second, before helping Pique and Ousmane Dembele get on the scoresheet.
The build-up was marred by clashes between Lyon fans and Catalan police in the hours before the game, with Spanish reports claiming five fans were injured and six were arrested.