The 22-year-old Mexico striker - nicknamed "little pea" - took Federico Macheda's low cross and drilled the ball past Cesar Sanchez in the 85th minute to secure only United's second victory in 19 away European matches against Spanish opponents.
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United, held 0-0 at home by Rangers in their opening match, moved joint top of Group C with the Scottish champions on four points. Valencia, the Spanish league leaders, are third with three points after their opening 4-0 win at Bursaspor.
"You've got to give us credit for the way we defended," United manager Sir Alex Ferguson told a news conference.
"They're not top of the league for nothing so for us to win here tonight is a good result for Manchester United."
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Neither side showed much creativity on a pleasantly warm night at the Mestalla, although Valencia improved in the second half, roared on by the passionate home support thronging the steeply-banked arena.
Strikers Dimitar Berbatov for United and Roberto Soldado for the home side cut lonely figures up front at times, although Berbatov forced a smart save from Sanchez when through on the Valencia keeper soon after half-time.
RARE SPARK
Valencia midfielder Pablo Hernandez was a rare spark of creativity and zest for the home side and had several good chances in either half.
His long-range effort whistled over the crossbar in the 16th minute before United goalkeeper Edwin Van der Sar misjudged a cross and Soldado headed narrowly over the open goal.
The introduction of striker Aritz Aduriz lifted the home crowd but Valencia were unable to find the net against a resolute United defence strengthened by the return of Rio Ferdinand from injury.
"His experience helped us, I don't think there's any question about that," Ferguson said of Ferdinand, who has been sidelined with a knee injury.
"It's his first real game for a long time and we have to be very pleased with that."
United, missing injured striker Wayne Rooney and experienced midfielders Paul Scholes and Ryan Giggs, had failed to score on their last three trips to Spain but Hernandez came close to a goal immediately after replacing Anderson in the 77th minute.
He slid in at the back post and struck the ball against the outside of the upright before beating Sanchez from Machado's accurate centre to snatch the three points.
