The Argentinian headed home midway through the first half, making his side's domination count.
Levante, in a more comfortable position than their opponents in the Primera Division table, played with less urgency and offered little throughout the 90 minutes, but were given the chance to equalise through a second-half penalty. However, Jose Javier Barkero could not take advantage from the spot.
Celta, lifted by their last-gasp win over Real Zaragoza last Monday, began the game the hungrier of the two sides and took a deserved lead on 20 minutes.
Denmark international Michael Krohn-Dehli showed great skill down the left wing to beat a defender and then swung in a cross towards the back post, where Fernandez was waiting to head the ball in.
The Argentinian could have scored another goal a few minutes later but this time aimed his header too close to Navas, who caught the ball comfortably.
Iago Aspas, returning to action after serving a four-match ban for violent conduct, had a chance to double the lead early in the second half when he found himself through on goal with Navas, but could not beat the goalkeeper, and when he lost the ball he took a dive after a challenge from Loukas Vyntra. The referee was not fooled and gave him a yellow card.
The forward had another chance to score a few moments later but failed to get on the end of a deep cross by Krohn-Delhi by inches.
Levante were handed a lifeline when they were awarded the softest of penalties, given for a push by Jonny Castro on Robert Acquafresca.
Barkero stepped up to take the kick but hit it wide of the right-hand post.
Acquafresca later headed over the bar after a corner in one of few chances for Levante, but the home side gave their opponents a nervy finish.
In injury time Celta goalkeeper Javi Varas came out to punch a cross, which fell towards Simao Mate, who volleyed the ball towards goal but Varas tipped it over the bar, allowing his side to hold onto their lead and, most crucially, the three points.