The home side might have taken the lead barely a minute into the match when Martins advanced on goal, but he fired his effort wide of the post.
Levante continued to create chances in the early stages and David Navarro came close with a powerful header with 10 minutes on the clock.
The home side did eventually take the lead after 22 minutes when Martins pounced on a loose ball inside the box to fire home from close range.
Valencia's best chance of the first period fell to Tino Costa 10 minutes before the break, but his effort from close range was blocked.
Levante twice came close to extending their lead moments into the second period when Nabil El Zhar advanced on goal, but he was denied on each occasion.
Chances remained few and far between as the match advanced its latter stages, with the home side hanging on to secure a vital three points in the context of their season.