Martins scored the only goal of the match midway through the opening half, controlling his goalkeeper's long boot downfield before powering the ball home high into the net.
Victory maintains Levante's unbeaten start to the season on home turf, while Valencia remain without a win on their travels and could slip closer to the relegation zone before the end of the day.
The three points came as a timely lift for Levante, who were hammered 4-0 at Osasuna last weekend before contriving to throw away a lead to lose 2-1 at 10-man Hannover in the Europa League in midweek.
Martins was into the action for the hosts inside the opening minute with a shot that whistled wide, while with nine minutes gone David Navarro's header was saved by Valencia goalkeeper Vicente Guaita.
Valencia threatened for the first time in the 12th minute when Roberto Soldado's shot was tipped round the post by Gustavo Munua, while from the resulting corner the dangerous striker saw a header flash just wide.
Tino Costa brought another stop from Munua moments later, but with 22 minutes gone Los Che found themselves a goal down, with Levante's goalkeeper playing a big part in the build-up.
Munua's long kick downfield sat up perfectly for Martins, who raced beyond the last defender and controlled the ball on his chest before lashing home a ferocious left-footed finish high beyond the helpless Guaita.
Valencia struggled for a response after going behind, with Jonathan Viera and Fernando Gago wasteful with what chances the visitors created early in the second half.
Soldado saw a header comfortably saved by Munua with 11 minutes remaining as Valencia's last chance went begging, while Levante might have extended their lead in the final 10 minutes when Pedro Rios drew a good save from Guaita.