The hosts worked the first opportunity of the night from a free kick on 15 minutes, with Javier Hernandez nearly getting on the end of Juan Mata's whipped free kick, but Diego Alves came out to claim the ball ahead of the Mexico international.
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United were beginning to string together some nice passing moves, and Ander Herrera tried his luck from distance following one such flowing piece of play, only for his effort to end up wide of the target.
Herrera picked out Ashley Young shortly after the 30-minute mark, and the winger found Wayne Rooney inside the box who was subsequently nudged in the back leaving the referee no choice but to point to the spot.
Rooney brushed himself down but was unable to fire United ahead, striking the post with his spot kick. The striker almost redeemed himself before the interval, although he was unable to control Darren Fletcher's pass on the edge of the area and another chance passed by.
It did not take long for the Red Devils to take the lead in the second half, however, thanks to Fletcher's strike which looked to take a deflection on its way past Alves.
Young almost doubled his side's lead shortly before the hour when played through one-on-one, but he made the wrong choice when in on goal and was dismissed in possession by the retreating Antonio Barragan.
The missed opportunity soon proved costly when Rodrigo tucked the ball home following a poorly defended set piece into the United box. Both Herrera and Tom Cleverley failed to deal with the ball, and the striker was left to level up the contest.
Both sides had opportunities to win the game in the final 20 minutes, but Valencia really should have secured victory if not for De Gea who smothered Paco Alcacer's close-range hit after initially parrying a shot.
The stop proved decisive as in the dying seconds substitute Fellaini prodded the ball into an empty net to claim his first United goal after Alves failed to claim a cross.
Van Gaal's side now turn their attention to Saturday's Premier League opener against Swansea City.