Cameroon international Samuel Eto'o put Mallorca ahead from the penalty spot 15 minutes from time and fellow striker Arnold Bruggink made sure of a first ever league win at the Riazor when he hooked in over Depor keeper Jose Molina just before the final whistle.
But leadership rivals Valencia were unable to take advantage of Deportivo's slip-up, managing only a draw against an improving Celta.
Deportivo lead the table on 21 points, just one ahead of Real Madrid, who were held to a 0-0 draw by Real Zaragoza on Tuesday, and third-placed Valencia.
Osasuna retained their surprise fourth place, three points further back, after a determined 2-0 win at home to Real Betis, while Barcelona moved up to fifth following a convincing 3-0 victory over Murcia, their first home win of the season.
Argentine striker Javier Saviola completed a slick passing move with a fine left-foot finish late in the first half, midfielder Xavi added a second after the break and Ronaldinho wrapped up an important win 11 minutes later.
The Catalans are now five points behind leaders Deportivo.
At the other end of the table, Javier Clemente's Espanyol claimed their first win of the season with a narrow 1-0 win away to Racing Santander, but the Barcelona-based side remain bottom of the table with just five points from nine games.
DETERMINED START
Mallorca, looking for their first win in seven outings, were in determined mood at the Riazor as they hounded Depor off the ball and dominated the possession in the early part of the game.
Midfielder Jovan Stankovic skimmed the bar with a well-struck free kick on 17 minutes and then hit the woodwork with a 20-metre curler.
Depor were restricted to isolated chances at either end of the half, midfielder Victor hitting the bar with a free kick on nine minutes and forward Albert Luque slamming a fierce shot against the post from an acute angle just before the break.
Mallorca finally got the breakthrough when Depor defender Enrique Romero conceded a penalty after pushing Fernando Correa inside the area.
Eto'o, who this week voiced his desire to leave Mallorca at the end of the season, drilled home from the spot.
Depor pushed forward but were caught out on the break when former PSV Eindhoven striker Bruggink raced on to a lofted pass and poked the ball over Molina who was off his line.
Argentine playmaker Pablo Aimar scored a rare header to give Valencia the lead against Celta just before the break at Mestalla, but the visitors hit back when defender Eduardo Berizzo rifled home from the edge of the area early in the second half.
Celta then took the lead when midfielder Jesuli burst through the Valencia defence to latch on to a Alexander Mostovoi pass before cracking home with his left foot but Fabio Canobbio guided equalised two minutes later.
