Los Che rescued an invaluable point against Marcelo Bielsa's side in a dramatic draw at the Mestalla Stadium where both sides had chances to steal victory.
The former Real Madrid striker notched two minutes from time, sneaking in his shot from a tight angle, and based on chances created a share of the spoils was probably the most accurate result.
Valencia started positively, spurning two chances inside the opening minute as it searched for an early breakthrough while Sergio Canales wasted a well crafted chance soon after.
Bilbao began to influence the game, though, and Fernando Llorente came close to punishing the home side when he pushed the ball wide of the target following Muniain's delightful through ball.
With halftime approaching, Gorka Iraizoz gifted Valencia a wonderful chance to take the lead when his clearance fell at the feet of Jonas. The ball reached the Brazilian quickly and he brilliantly directed his effort towards goal, the custodian was saved from embarrassment when the ball ricocheted off the post.
Valencia emerged for the second half in high spirits and Jonas should have put the team ahead when Jeremy Mathieu's low cross worked its way to the Brazilian six yards out only for him to scoop the ball over the crossbar.
Roberto Soldado was denied a clear penalty in the 67th minute when he was hurled to the ground only for the referee to wave away the striker's claims for a spot-kick, and Valencia found itself behind soon after.
Pablo Hernandez gave the ball away to Muniain 25 yards from goal, and the Spaniard instinctively headed towards goal. He touched the ball inside of Ricardo Costa before firing an unstoppable right-foot shot past Guaita into the top corner.
Valencia searched for an equalizer and the club was eventually rewarded two minutes from time when Soldado latched onto Ever Banega's through ball, the Spanish striker touching around the onrushing Iraizoz and squeezing the ball in from the tightest of angles to level the match.
Muniain spurned a late chance to steal all three points for Bilbao but in the end Valencia had done enough to rescue the match.
Los Che head to Zaragoza in midweek as they will look to return to winning ways while Bilbao will search to stretch its unbeaten run to five games when it hosts Atletico Madrid.