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.
FULL-TIME: There's the whistle! Leo Messi scores twice as Barça battle back from 2-0, first-half deficit to earn a tie!— FC Barcelona (@FCBarcelona) February 2, 2019
FT: Barça 2 - 2 Valencia
#Messi 39' (p.), 64' / Gameiro 24' , Parejo 32' (p.)
What does it mean? 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.
Champions a shambles in defence
It would be unfair to single out just one Barcelona defender as they were collectively dreadful in the first half. Gerard Pique teed up Valencia's first effort on goal almost from the kick-off, while all four players were then caught out as Rodrigo advanced for the opener. Roberto's actions for the penalty were senseless, to say the least.
Key Opta Facts
Messi is the third player in LaLiga history to score 50 penalty goals, after Cristiano Ronaldo (61) and Hugo Sanchez (56).
Messi has scored in each of his last nine games for Barcelona in all competitions (12 goals), his best goalscoring run since January 2013 (10 games).
Parejo has been involved in six goals in his last eight games in LaLiga (four goals and two assists).
Messi has scored more goals from outside the box than any other player in Europe’s top five leagues this season (six goals).
Only against Sevilla (25) has Messi scored more goals than against Valencia (24) in LaLiga.
Barcelona's focus will now shift to the first of three Clasicos in the space of a month, welcoming Madrid to Camp Nou in a midweek Copa del Rey semi-final first leg. Valencia visit Betis next in the same competition.