Villarreal looked to have breathed life back into LaLiga's title race after they came from 2-0 down to lead 4-2, but substitute Messi – who had been rested – and Suarez remarkably secured a share of the spoils to keep Barca eight points ahead of Atletico Madrid ahead of their meeting on Saturday.
A thrilling first half saw Barca race into a 2-0 lead against the run of play, with Philippe Coutinho and Malcom finding the net, but Samuel Chukwueze deservedly got Villarreal back in the contest after a rapid counter and a Marc-Andre ter Stegen error allowed Karl Toko Ekambi to level just after the break.
Goals from Vicente Iborra and Carlos Bacca appeared to put the contest beyond Barca, but Messi found the net with a brilliant free-kick in the 90th minute and Suarez broke Villarreal hearts in the third minute of stoppage time with a rasping finish.
Villarreal made a promising start, testing Ter Stegen twice inside the first 10 minutes, but Barca carved through them soon after – Malcom squaring across goal for Coutinho to finish.
Malcom was decisive again with 16 minutes played, meeting Arturo Vidal's cross with a looping header into the right side of the goal.
Coutinho hit the post a few moments later and Villarreal soon capitalised with a devastating break, as Chukwueze neatly slotted home after his initial effort came back off the upright.
Chukwueze played a role again early in the second half, releasing Toko Ekambi up the right flank and his sliced cross punished Ter Stegen's poor positioning as it crept in at the near post.
Iborra put Villarreal ahead for the first time just past the hour, clipping past Ter Stegen from Manu Morlanes' incisive pass, before Bacca seemingly finished the champions off towards the end in rounding the German and slotting home.
But Messi – shortly after the hosts' Alvaro Gonzalez was dismissed for a second booking – blasted a 20-yard free-kick into the top-left corner at the end of normal time.
And Suarez rescued Barca with almost the last kick of the game, his sweetly struck left-footed half-volley from 18 yards giving Sergio Asenjo no chance.
Messi the catalyst…again
For a while, it looked as though Messi's impact from the bench was going to be minimal, but, as he often does, he found a way to inspire Barca in adversity. His goal – which came from a free-kick he won – was as brilliant as it was inevitable, and that spurred Barca on to pile the pressure on for the rest of stoppage time.
