Michel and David Villa were on target for the hosts at the Mestalla, while Villa also saw a penalty saved by substitute goalkeeper Lukasz Fabianski.
After a tight first half played for the most part in driving rain, the home side came alive after the break with Villa - still in the Valencia ranks despite a summer of transfer speculation linking him with a move away - combining well with fellow Spain international Joaquin.
The pair came close to breaking the deadlock after 56 minutes when Villa's cheeky backheel into Joaquin's path ended with the winger drilling in a rasping shot that was smartly parried by Fabianski, a half-time replacement for Manuel Almunia.
Fabianski was again called into action midway through the half after Mikael Silvestre conceded a penalty for a foul on Michel, the young custodian guessing correctly to save Villa's penalty diving to his right.
Cesc Fabregas was called into action to clear a header off the line as Valencia began to dominate, and the deadlock was finally broken 15 minutes from time.
Michel claimed the goal, the midfielder following up to score after Villa's initial effort from a low right-wing free-kick had been blocked by the Gunners' defence.
The hosts made it 2-0 at the death, although they were helped by an injury to Fabianski, who appeared to have a calf problem.
There was no mercy from the Valencia players, though, and when Villa got in behind the defence to latch onto Joaquin's through ball there was only going to be one outcome, the striker firing through the legs of the ailing Fabianski to seal the win.