The Andalusians outmuscled their opponents and even managed to endure the final 35 minutes without conceding despite being reduced to 10 men when Duda was shown a straight red card.
The 2-0 victory marks Malaga's second straight away win and sees them move onto 32 points, just one point behind Celta with nine games left.
Celta had far superior possession but were frustrated by an alert Malaga defence, and were punished due to their own frailties at the back, failing to deal with crosses into the box on more than one occasion.
Michael Krohn Dehli came close to giving the hosts the lead with 14 minutes played, smacking the crossbar after an interchange with Nolito. Two minutes later it was Malaga cursing their luck, Samuel hitting the bar.
Nordin Amrabat then had a goal harshly ruled out for offside, but the visitors only had to wait a few more minutes before taking the lead.
Duda delivered a cross into the six-yard area and Yoel could not properly clear the danger, allowing Camacho to knock the rebound in from a few yards out.
The Celta players' appeals for offside against the midfielder could not persuade the referee to rule the goal out, and the hosts were soon two goals down. This time slack marking allowed Camacho to wander into the path of a free-kick from Duda, diving unchallenged to head home the cross.
Celta had lacked ideas and Luis Enrique brought on Rafinha immediately after the break in an attempt to give his side more creativity. However, the midfielder was not able to help his side break down their opponents.
Nolito attempted to find a way back into the game for the hosts early in the second half, but his free-kick sailed high over the bar.
Roque Santa Cruz should have added a third for Malaga, narrowly failing to connect with the ball as he slid in to meet a free-kick swung in by Duda.
The Portuguese midfielder had been one of Schuster's strongest performers but was sent off for kicking out at Rafinha, taking out his anger on the Barcelona loanee after failing to win a free-kick when he was brought down.
Celta's football improved with an extra man on the pitch but they were unable to profit from their advantage. Charles' headed goal was correctly ruled out for offside, while Levy Madinda flashed a shot wide of the far post after breaking into the area with two minutes to go.