The hosts had to play for almost an hour with a man less as Mikel Rico was shown an extremely harsh second yellow card when referee Alberto Undiano Mallenco adjudged him to have handled 11 minutes before half-time.
Despite that blow it was Granada who struck first just four minutes after the break as substitute Brayan Angulo sent a perfectly looping volley over Dani Alves.
The lead, though, only lasted nine minutes as Jonas bulleted home a header from Piatti's corner and the Argentinian then scored himself as he redirected Roberto Soldado's cross-shot into an empty net eight minutes from time.
The win kept Valencia in the chase for fourth place in the Primera Division as they closed the gap on Real Betis and Malaga to four points, while Granada remained just a point above the relegation zone.
As had been the case in their games just before the winter break, it was Granada who made most of the early running, but they were again made to pay for Odion Ighalo's lack of quality in front of goal.
The Nigerian first just failed to reach Allan Nyom's dangerous cross before then meekly heading his side's best chance of the first half straight at Diego Alves.
Valencia had not created a huge amount either, with Piatti's low drive that was turned behind by Roberto as close as they came.
But the visitors were handed a huge boost after 34 minutes when Rico, who had already been booked for a late challenge on Soldado, was deemed to have stopped a Valencia counter-attack by using his arm, despite replays showing the ball had clearly hit the midfielder's shoulder.
Granada were dealt another blow seconds before the break as Dani Benitez had to be stretchered off, but his replacement made an immediate impact when the second half got under way as Angulo pounced on a poor defensive header just inside the box to volley home his first goal for the club.
The goal seemed to spur Valencia into action and they were level soon after as Jonas showed great strength and determination to meet Piatti's corner and head just inside the near post.
Indeed the Brazilian could have had a hat-trick as he pulled another effort wide and was also denied by a fine save by Roberto, while Nelson Valdez also shot just over as Los Che pilled on the pressure in search of a winner.
It arrived with just eight minutes remaining as Valdez fed Soldado and his drive back across goal was slotted into the net by Piatti.