The hosts' captain rolled home a penalty on the hour mark, after Pablo Piatti had been bundled over in the box, before their No.9 sealed victory with a near-post tap-in
Los Che struggled to break their visitors down during an uninspiring first half at Mestalla but Parejo broke the deadlock on the hour mark with a penalty, after Pablo Piatti had been bundled over in the area.
Nuno Santo's men then made the game safe 12 minutes later when Sofiane Feghouli teed up Paco for his sixth Liga goal of the season.
Valencia started strongly, with Alvaro Negredo testing Fabricio inside the opening 60 seconds before calling the goalkeeper into action again in the 13th minute with a header from a corner.
However, Deportivo frustrated the hosts for the majority of the first half, albeit without offering any threat whatsoever on the counterattack.
Valencia, though, looked far more menacing after the break and finally opened the scoring in the 60th minute.
Piatti deserved much of the credit for the breakthrough as the diminutive winger was upended in the area by Juanfran.
The Argentine had seen a low strike spilled by Fabricio in the Depor goal and he was the first to the rebound, positioning his body in front of the ball, thus forcing Juanfran to go through him as he desperately tried to clear.
Parejo took care of the resulting spot-kick with the minimum of fuss, sending Fabricio the wrong way with a low strike to the keeper's right.
Valencia made the game safe in the 72nd minute - and again, Piatti was involved, pouncing on a loose ball in the box before allowing Feghouli to take possession and square for Paco, who side-footed home at the near post.
Depor tried to rally, with Alex Bergantinos trying his luck with a header from the edge of the area that Diego Alves had to tip over the bar.
However, Valencia cruised through the final quarter to claim a win that moves them two points above Atletico, who travel to Catalunya to face Espanyol on Saturday.