The Qatar-owned club fell behind in the 24th minute to a Philippe Coutinho strike before former Manchester United and Real Madrid forward Ruud van Nistelrooy netted a 75th-minute equaliser moments after coming off the bench.
Malaga snatched the winner two minutes later when Espanyol goalkeeper Francisco Casilla saved Salomon Rondon's header only for Martin Demichelis to smash the loose ball into the net.
"We are on a good run of form and losing a few matches earlier in the season has helped inspire us to go for victory in every game," Malaga coach Manuel Pellegrini told a news conference after his side's fifth win in six games.
"Every point is very valuable because the standings are very congested," the Chilean added.
The victory lifted the Andalusians, one of Europe's biggest spenders in recent seasons, into Spain's fourth Champions League qualification place above Levante, who were beaten 2-0 at home to an Osasuna side also in the running.
With nine games remaining, Valencia, who lost 3-1 at Getafe on Saturday, hold on to third on 47 points thanks to a superior goal difference over Malaga and Levante stay three points behind and drop to fifth.
Leaders Real Madrid preserved their six-point advantage over second-placed Barcelona with a 5-1 drubbing of Real Sociedad on Saturday after Barca had shrugged off the dismissal of Thiago Alcantara early in the second half to win 2-0 at Real Mallorca.
Real have 75 points and Barca, chasing a fourth successive La Liga title, have 69, 22 ahead of Valencia and Malaga.
TOSS UP
Osasuna are a point behind Levante in sixth, three ahead of seventh-placed Espanyol, while Atletico Madrid are eighth, level on 39 points with Getafe, after they conceded a penalty in added time and lost 1-0 at a resurgent Real Zaragoza.
Zaragoza, whose season has been overshadowed by financial problems and institutional strife, drew level with fellow struggler's Sporting Gijon and Racing Santander on 25 points but remained rooted to the bottom and six points from safety.
Gijon scored a late equaliser in a 1-1 draw at Athletic Bilbao, while Santander also came from behind to earn a point in a 1-1 stalemate at Real Betis.
"The only thing we can do is remain humble and maybe we have a chance of saving ourselves from relegation," Zaragoza coach Manolo Jimenez told a news conference.
"At the end of the game with the heat and the very dry pitch it was a toss-up whether we won or lost and it was clear that whoever scored would take the three points," he added.
Bilbao are 10th on 38 points and Marcelo Bielsa's side are without a win in three matches since they knocked Premier League side Manchester United out of the Europa League on March 15.
Villarreal's 2-0 win at Rayo
