Valencia, who headed into the recent winter break with three defeats in four matches, came close early on through a deflected Guedes shot.
Guedes and Borges had further shots helped aside as the first half transpired, but Los Che - with debutant Francis Coquelin in their ranks - did grab a goal before the break through their influential Portuguese winger.
A long-range drive somehow found its way into the net due to some poor goalkeeping, and Valencia added a second to their tally from their first serious move of the second half.
Rodrigo this time got the better of Ruben with a deflected shot, which was assisted by star man Guedes to give the high-flyers some breathing space.
Ruben was needed to thwart Guedes again soon after, while also keeping out Simone Zaza, and those latest saves would prove key as Andone converted from close range with two minutes to play.
There was to be no late comeback, though, with Adrian hammering the ball over the crossbar from five yards out in the dying seconds.
DEPORTIVO LA CORUNA (4-3-3): Ruben; Juanfran, Albentosa, Sidnei, Luisinho; Borges (Colak 52'), Guilherme, Mosquera (Valverde 70'); Lucas, Andone, Adrian
VALENCIA (4-4-2): Neto; Gaya, Garay, Paulista, Vezo; Coquelin (Montoya 83'), Parejo, Maksimovic, Guedes; Mina (Vietto 74'), Rodrigo (Zaza 81')