Valencia have rebuilt their team with the pending arrival of Singapore billionaire Peter Lim but it was two youth products who paved the way for victory.
Alcacer, who scored on his competitive international debut for Spain earlier this month against Macedonia, demonstrated his predatory skills with a flicked header into the top corner after 22 minutes from a Sofiane Feghouli cross.
Minutes later left back Gaya drove in a loose ball from inside the penalty area for his first league goal.
Cordoba, who returned to the top flight this season and are bottom with two points, struggled to cope with Valencia's onslaught and Feghouli wrapped up the win in the second half, latching on to an Andre Gomes pass to finishing clinically.
"The team is playing very well at the moment and knows what it wants in each game. We are creating chances and we are where we are for a reason," Alcacer told reporters.
"Our target since the arrival of the coach Nuno (Espirito Santo) has been perfection and while we are following that line we are not dreaming of being at the top but concentrating on each match."
Valencia have won their last four games and are level with Barcelona and Sevilla on 13 points but have scored more goals.
In the day's other fixture Espanyol won their first match of the season with goals from Sergio Garcia and Christian Stuani giving them a 2-0 victory over Getafe.
(Editing by Martyn Herman)
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