Oriol Riera scored the only goal of the game as Los Rojillos secured just their second win of the season and ended Malaga's five-game unbeaten run in the process.
Bernd Schuster's side had scored seven goals without reply on their way to winning their previous two home games, while Osasuna were yet to pick up an away point prior to kickoff.
However, it was Osasuna who opened the scoring against the run of play when Riera beat Willy Caballero to net his third goal in his last four outings.
The visitors were buoyed by taking the lead and could have gone into the break with a more comfortable advantage, but Caballero saved from both Riera and Francisco Silva.
There were few clear sights of goal in the second period for Malaga, who committed bodies forward in stoppage time, but came up short in their search for an equaliser.