The hosts could have been back on level terms just four minutes later but David Barral's strike found the crossbar from a few yards out, and his headed follow-up was ruled out for offside.
On the stroke of 90 minutes, Los Che doubled their advantage when Alcacer managed to latch on to a poor backpass down the right. His initial effort was palmed away by keeper Andres Fernandez but the deflection was found by Santi Mina, who was rewarded with a hug from a jubilant Neville.
The clash was not without even more late drama as Edgar Mendez quickly pulled one back for the hosts, heading in from a free kick in the second minute of time added on to ensure a nervy finish.
It proved mere consolation, however, as Valencia held on for the three points to move up to 11th in La Liga, while Granada sit four points from safety in 19th.