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.
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 said.
"In five years, we have only won once here. A draw is a fair result."
Barca levelled before the break when Joao Pereira needlessly fouled Pedro in the area and Messi arrowed a penalty high into the top corner.
Cesc Fabregas went close and Andres Guardado forced a flying save from Valdes but Barca were in the ascendancy.
Atletico had leading scorer Radamel Falcao back from injury but it was combative striker Costa who scored from close range in a bruising encounter against Betis.
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.
Young playmaker Isco, who agreed an improved contract with the south-coast club during the week, levelled from the penalty spot in the 23rd minute and both sides hit the woodwork.
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 some 15 months on the sidelines with injury.
Zaragoza had midfielder Jose Mari sent off for a second bookable offence near the end.
Rayo Vallecano also failed to close on the top sides when they lost 2-1 at improving King's Cup semi-finalists Sevilla.
Betis are fifth with 35 points, Valencia sixth on 34, the same as seventh-placed Rayo, and Real Sociedad are eighth with 33 after a 3-0 home win over 10-man Real Mallorca.