Malaga moved level with Valencia in third spot on points as Nacho Camacho's first-half header was enough to earn all three points from a scrappy encounter at La Rosaleda.
The hosts dominated the opening period and Vicente Guaita had to be alert to turn Eliseu's drive on to the post before Camacho opened the scoring with a towering header from Jesus Gamez's cross just before the half-hour mark.
Things got even worse for Valencia when Sofiane Feghouli was dismissed for a second bookable offence just after the hour and Malaga were only denied a more comprehensive victory by a combination of the woodwork and some fine goalkeeping by Guaita.
The game failed to live up to the quality expected of a clash between the third and fourth-placed teams in the league as Valencia appeared jaded after their midweek UEFA Europa League exit to Atletico Madrid, while Malaga lacked the killer instinct that has dogged them all season.
However, it was the home side who were the more progressive in the early stages and Eliseu's left-footed effort from the edge of the area had Guaita at full stretch to turn the ball on to the frame of the goal. Thirteen minutes later, Malaga did have the lead as Camacho's late run into the area was not tracked by the Valencia midfield and his looping header this time gave Guaita no chance.
The Valencia goalkeeper was called into action again just before half-time to repel Santi Cazorla's powerful strike, while at the other end Ricardo Costa headed the visitors' only effort of the first half just wide from Tino Costa's corner.
Malaga had three opportunities in quick succession to extend their lead at the start of the second period, but Cazorla and Joaquin both fired straight at Guaita and Jose Salomon Rondon blazed his shot well wide with the clearest opening after robbing Adil Rami of possession in a dangerous area.
Set-pieces continued to be Valencia's best chance of a way back into the game and Rami just could not get over another wonderful delivery from Tino Costa as he headed over on 58 minutes. Moments later, though, any chance of a Valencia comeback was all but extinguished as Feghouli was shown his second booking of the afternoon for raising his elbow as he contested a header with Eliseu.
Isco should have done better when he pulled his shot wide from the edge of the area, but there was little wrong with Duda's fierce drive from 25 yards 20 minutes later that came back off the bar. Guaita made one more great save to deny Ruud Van Nistelrooy only his fourth goal of the season in stoppage time, but the hosts were never in any danger of letting their lead slip as they took a big step towards qualifying for the UEFA Champions League for the first time in their history.