Manu Vallejo scored the decisive late goals in a goal-fest at Mestalla after Jose Luis Morales's double for Levante had been cancelled out by Gabriel Paulista and the excellent Maxi Gomez.
The victory was Javi Gracia's first since being appointed Valencia coach in July and gets the team off to a positive start in La Liga, despite simmering tensions off the pitch.
Manuel Pellegrini also enjoyed a successful start in charge of Real Betis after they won 1-0 away at Alaves. But Unai Emery's first game as coach of Villarreal ended in a 1-1 draw at home to newly-promoted Huesca.
Valencia would hope to be challenging the likes of Villarreal for a place in the top four this season but several key players have been sold, with unpopular owner Peter Lim determined to improve the club's financial situation.
Gracia said on Friday he felt "sad" because the squad had been "weakened", a brave move given the board's impatience with previous coaches.
Yet this was a gutsy performance that Gracia could have been proud of, even if Valencia were behind after just 37 seconds, Morales weaving his way through four defenders before poking in.
Gabriel pulled Valencia level when his header crept inside the near post from a corner but Levante scored again, Morales driving into the top corner after more sloppy Valencia defending.
But Valencia came back again, Maxi sliding a shot into the far corner and then Yunus Musah, the 17-year-old who left Arsenal's academy last year, clipped the crossbar with a shot in the second half.
Valencia looked more likely to snatch a third and Vallejo kept a cool head when it mattered, tucking a finish into the corner after a smart dummy by Maxi.
There was time even for a fourth in injury-time as Maxi pulled clear on the break and when his shot cannoned back off the post, Vallejo was perfectly placed.