World Player of the Year Messi grabbed his 34th league goal from the penalty spot just before half-time at the Mestalla after Ever Banega had given the livelier hosts a 33rd-minute lead.
Atletico substitute Diego Costa nodded in from a 61st-minute corner to maintain their perfect home record, lifting them seven points clear of city rivals Real Madrid in third.
Barca have 59 points from 22 games, Atletico 50, and the champions have 43 after losing 1-0 at lowly Granada on Saturday when Cristiano Ronaldo headed the game's only goal into his own net.
Valencia's intense pressure seemed to unsettle Barca, who looked sluggish after Wednesday's King's Cup semi-final first leg at the Bernabeu, which they drew 1-1.
Their aggression paid dividends when Gerard Pique's weak headed clearance fell to Banega in the area and the Argentine midfielder fired a low shot under Valdes.
"It's possible we were suffering a bit from the Madrid game, but I would point out the work of our rival," Barca assistant coach Jordi Roura told reporters.
"In five years, we have only won once here. A draw is a fair result."
Another ruthlessly efficient performance ensured Diego Simeone's side made it 12 wins from 12 in the league at the Calderon with only six goals conceded.
Earlier, fourth-placed Malaga failed to make the most of Real's slip-up when they could only manage a 1-1 draw at home to Real Zaragoza to move on to 36 points.
They had to come from behind after Helder Postiga's 13th-minute volley put the visitors ahead at a sun-drenched Rosaleda.
Manuel Pellegrini's side never really had complete control of the game, and there was no fairytale return for Brazilian forward Julio Baptista, who came on as a second-half substitute after 15 months on the sidelines with injury.
Rayo Vallecano also failed to close on the top sides when they lost 2-1 at improving King's Cup semi-finalists Sevilla.
