Sergio Canales' fine early goal was sufficient to seal victory, though forwards Roberto Soldado and Jonas Goncalves wasted a hatful of chances to extend the lead.
And they should have been made to pay by Carlos Martins late on, while Inigo Lopez hit the bar as Granada improved in the second period.
Little more than three minutes were on the clock before Canales gave the home side the lead, firing home low left-footed from 25 yards after being teed up by Pablo Piatti.
Soldado went close to a second when Canales took a short corner and crossed for the striker to head goalwards, keeper Roberto showing excellent reflexes to tip the ball over.
That save was almost immediately replicated by opposite number Vicente Guaita after Daniel Benitez swung a free-kick from wide on the right directly at goal.
Roberto made a sharp save from Ever Banega before Guaita fielded another Benitez curler at the other end.
Referee Eduardo Iturralde Gonzalez was at the centre of the attention on the half-hour when he slipped and inadvertently affected a two-footed challenge on Canales, who accepted the official's apology with a wry smile.
Canales blazed over and Pablo was denied by Diego Mainz's block, while Roberto saved from Banega right on half-time.
Soldado volleyed Jeremy Mathieu's cross over and Piatti's low ball flashed dangerously across the six-yard box as Valencia continued to press after the interval.
But Granada found their way into the game and Alexandre Geijo's 25-yard effort bobbled just wide of the left post. Geijo then delivered a corner from which Inigo Lopez's downwards header bounced up and struck the bar.
Valencia should have killed the game off when Soldado slid in to meet Jonas' cross, but he skied the ball over the bar at full stretch.
And Granada missed an equally good chance when Martins broke through a gap in the Valencia defence but dallied on the ball and failed to get his shot away before going down under minimal contact from Adil Rami.
Roberto saved from Jonas again and repeated the feat once more as the clock ticked past 90 minutes, though the forward should certainly have scored on that occasion after being teed up eight yards out by Soldado.