The Blaugrana captain was in inspired form after it looked as though Ernesto Valverde's call to shuffle his pack would see his side come away empty-handed as they deservedly trailed to efforts from Kevin Gameiro and Daniel Parejo.
The league leaders rallied and Messi scored either side of half-time to clinch a point in a match packed with incident.
Atletico Madrid can now close to within three points of top spot if they beat Real Betis on Sunday, but Barca at least avoided embarrassment ahead of facing Real Madrid in the Copa del Rey on Wednesday.
Barcelona failed to heed early warnings as Marc-Andre ter Stegen made an instinctive stop from Parejo and watched Denis Cheryshev strike the post, before Rodrigo Moreno fed Gameiro to smash in the opener.
It was two when Sergi Roberto shoved Daniel Wass to the ground in the area and Parejo scored from the spot - shortly after an outstanding Neto save at the other end - but a second penalty award breathed new life into Barca.
Referee Alberto Undiano Mallenco blew for a foul on Nelson Semedo moments before Messi arrowed the loose ball into the top corner, but the official's blushes were spared as the same man netted from 12 yards.
Roberto cracked the upright and Messi wastefully volleyed over as Valencia's defensive effort became increasingly desperate, although Rodrigo twice went close to a clinching third following the restart.
Predictably, it was Messi who made the Valencia forward pay, curling a low effort around two defenders from 25 yards.
Barca's talisman subsequently required treatment for an apparent thigh ailment, but he returned to see out the 90 minutes as his side fell short of completing the turnaround and claiming all three points.
Valverde pays for defensive changes
Approaching a key stretch in the season, with crunch Copa del Rey and Champions League matches to come and the title race a long way from over, Valverde's decision to leave Clenment Lenglet and Jordi Alba always looked a risky one. And his reshuffle at the back duly backfired as a dismal defensive showing granted Valencia a handsome first-half lead.
Messi magic makes the difference
Who else? Time and time again throughout his storied Barcelona career, Messi has come to the rescue. It was no different on Saturday as Valverde's men looked down and out after just over half an hour. The Argentina great peppered Neto's goal and got his reward, even atoning for an uncharacteristic close-range miss.
