Augusto Fernández secured the victory for Celta Vigo with his goal in the 20th minute, a header into the lower left of the goal after intercepting a pass from Los Granotes's Pedro López.
Celta de Vigo are now out of the relegation zone and into 16th place with a record of eight wins, 19 losses and six draws.
Levante now sit in 12th in the table with a record of 11 wins, 15 losses and seven draws.
In the late match Real Zaragoza earned a 3-2 win over Real Mallorca after a late goal from Rubén Rochina, who came on as a substitute, secured the victory.
Tomer Hemed put Mallorca ahead in the 11th minute, but a right-footed shot by Francisco Montañés in the 28th minute and a header by Helder Postiga in the 60th minute put the home side in front.
A right-footed shot by Javier Arizmendi in the 82nd minute looked to have given Mallorca a share of the points until Rochina's late winner two minutes from time.