Messi tried his luck with a first-time effort on the edge of the area after half an hour and goalkeeper Neto fumbled the shot, resulting in the ball crossing the line by about a yard, but referee Ignacio Iglesias Villanueva and his officials failed to spot it, effectively costing Barca two points.
Ernesto Valverde's men produced what was arguably one of their best halves of football so far this season in the first period, as they quickly got to grips with Valencia's intense style and asserted their dominance at Mestalla.
The officials took centre stage with their howler, though, before Barca's misery worsened after the break.
Valencia were significantly more threatening from an attacking perspective in the second half, resulting in Rodrigo turning home from inside the six-yard box.
Barca ensured they returned home with a point, however, as Alba made the most of a sublime Messi pass to keep the club's unbeaten start to the league season – and four-point lead over Valencia – intact, but there will be an undoubted element of frustration over the first-half controversy.
Barca looked to establish control early on by enjoying periods of keep-ball in the final third, but Valencia's aggressive pressing forced a few errors and provided some encouragement.
Ivan Rakitic was guilty of one of those mistakes, as his wayward pass back towards Thomas Vermaelen – starting in LaLiga for the first time in 22 months – was intercepted by Simone Zaza, but Samuel Umtiti made a vital last-ditch block to deny Rodrigo after he was fed by his strike partner.
Barca soon got to grips with Valencia's approach and began to dominate, but they were astonishingly denied the lead after half an hour.
Neto fumbled Messi's first-time 18-yard effort, before seeing the ball squirm through his legs and cross the line, but the officials failed to award the goal, leaving Barca apoplectic.
Valencia almost rubbed salt in the wounds by breaking down the other end on the counter-attack, with Zaza firing narrowly wide from the edge of the area.
The hosts began the second half with renewed urgency in the final third and put Barca under more of pressure, with Zaza shooting just off target again from 20 yards after good play by Goncalo Guedes.
Guedes caused trouble again just before the hour mark, running at Umtiti and skipping past him in the area, but Marc-Andre ter Stegen rushed out to block his eventual shot.
But Ter Stegen was helpless a few minutes later when Guedes found the overlapping Jose Gaya and his low cross was turned in from close range by Rodrigo.
The home fans were silenced in the 82nd minute, though, as a moment of genius from Messi ultimately provided Barca with the catalyst to salvage a result.
The Argentina star spotted the run of Alba into the area and clipped a marvellous pass into the left-back's path, and he duly provided a classy finish past the helpless Neto.
Valencia enjoyed some more late pressure and Zaza smashed a volley over the crossbar for one of the final touches of the match, but it finished all-square thanks in part to Villanueva's horrendous gaffe in the first half.
