Juan Antonio Pizzi's side, who cruised into the quarter-finals of the Europa League with a 4-0 aggregate win over Ludogorets on Thursday, ended a three-match winless streak in the league on Sunday, moving up two places into eighth as a result.
The defeat saw derby rivals Villarreal, who scored a late consolation through Giovani dos Santos, move down a place into seventh in the standings.
The home side started strongest and could have taken the lead had Federico Cartabia's close-range header been on target.
It did not take long for Villarreal to come into the game and Tomas Pina was unlucky his effort from the right of the penalty box sailed past the Valencia goal.
The home side lost Diego Alves to injury after 20 minutes and he was replaced by Vicente Guaita as the home side pressed forward.
Fifteen minutes later Fuego broke the deadlock for Los Che with a beautiful curled effort from just outside the 18-yard box, beating Sergio Asenjo to hand his side the lead.
And the 30-year-old midfielder struck again just before the break as he volleyed home from close range, sending his low shot into the back of the net.
The second half took a while to get going and Oliver Torres could have pulled a goal back for the visitors 10 minutes in but his effort from the edge of the box went wide.
Juan Bernat's drilled shot minutes later almost handed the home side a safety net had it not been deflected out, while Seydou Keita also came close to netting their third with a great close-range shot hitting the bar.
But it was the away side that hit the target as the game wore on with Dos Santos making no mistake with a superb touch in the box, as he curled the ball into the centre of the home goal in the final 10 minutes.