Marcelino Garcia Toral's charges continued to press and were rewarded with their second goal of the game just after the hour.
Levante then had the ball in the back of the net from a corner, but the referee ruled the goal out due to a push on a Valencia player, which replays showed came from a teammate.
The game was eventually put beyond the reach of Levante with a controversial late penalty awarded to Simone Zaza which was converted by Parejo.
VALENCIA (4-4-2): Neto; Montoya, Gabriel, Vezo, Gaya; Soler (Maksimovic 90+1'), Parejo, Kondogbia (Coquelin 73'), Guedes; Mina, Vietto (Zaza 79')
LEVANTE (4-1-4-1): Oier; Coke, Suarez, Postigo, Luna; Lukic (Marti 73'); Morales, Doukoure (Bardhi 72'), Campana, Alvarez, Pazzini body check tags ::