At Mestalla, the hosts took advantage of their one-man advantage by scoring all of their goals in the final 14 minutes, earning three priceless points
Entering the day level with Malaga on points in third place with 55, four strikes towards the end of the match allowed Los Che to move three points clear, as their rivals for the spot fell 4-1 to Barcelona earlier in the day.
In the opening stages of the match, each team failed to settle down quickly, and couldn't manage to create many attacking chances. On 10 minutes, Jordi Alba fired in a powerful effort after Jonas and Pablo Hernandez did well down the right to find the Spanish international, but his effort was blocked by a defender and sent out for a corner.
Thirty minutes in, the visitors had their clearest chance of the game, when Perez got down the left to send in a low cross into the heart of the box. He found Raul Garcia, who laid off a ball to Nino, who fired an effort to the right post that beat Vicente Guaita, but drifted wide of the post.
The entertainment continued during the break as Dejan Lekic was shown a red card for striking Adil Rami, after the two both received yellow cards minutes prior for a scuffle.
In the second half and with a one-man advantage, Unai Emery replaced Roberto Soldado with Aritz Aduriz. Valencia managed to consistently attack in the second half, reaching nearly 20 total corners but could not find the breakthrough until late on.
Jordi Alba sent in a cross just before reaching the byeline, finding Aduriz, who leapt to head the ball low into the right side of the goal for the advantage on 76 minutes.
Emery's men doubled up five minutes later on the counter, with Pablo chipping a ball into the box from the right that split several defenders, finding Jonas, who finished calmly at the left post.
Then, four minutes from time, Aduriz found his second in front of goal on the counter, when Piatti sent in a low cross right to the feet of the former Mallorca man, who netted calmly. Jonas got his double seconds later from close after Fernandez stopped a sliding Aduriz effort, completing the dominant second half display of Los Che.
With two matches left, Los Che host Villarreal on Saturday and can clinch third place with a win and if Malaga lose or draw.
Osasuna, who could have jumped into Europa League qualification zone with a win, sit in ninth place with 48 points and host Real Sociedad on Saturday.