Pacy Nigeria forward Martins, who joined last month from Russian club Rubin Kazan, sped on to a long clearance from Levante goalkeeper Gustavo Munua in the 22nd minute at the Estadio Ciutat de Valencia.
The former Inter Milan and Newcastle forward controlled the bouncing ball on his chest before smashing an unstoppable shot into the roof of the net past Vicente Guaita.
Valencia saw plenty of the ball but were toothless in attack and slipped to a third defeat in seven league outings this season, leaving them in 14th on eight points, two behind Levante who climbed to 11th.
The inexperienced Pellegrino, a former defender who played for Valencia and had a short stint at Liverpool, is in his first term in charge at the club after succeeding Unai Emery at the end of last season.
Under Argentine Pellegrino, Valencia lost their opening Champions League Group F match against last year's beaten finalists Bayern Munich but recovered to beat Lille 2-0 at home on Tuesday.