Philippe Coutinho had put hosts Espanyol ahead with a clever free-kick on 24 minutes, but they were fortunate to go into the break ahead after both Enzo Maresca and Isco struck the post.
Malaga would get their equaliser, however, in the 76th minute, as substitute van Nistelrooy scored with his first touch.
And the away team snatched a vital win when Demichelis netted just two minutes later, striking home after Francisco Casilla could only parry Salomon Rondon's header.
Meanwhile, Real Zaragoza secured three vital points in their bid to avoid relegation with a 1-0 win against Atletico Madrid.
Apono's stoppage-time penalty, awarded after Diego Godin's clumsy challenge on Helder Postiga, was all that separated the two teams at La Romareda.
Elsewhere, Osasuna consolidated sixth spot with a 2-0 win over fifth-placed Levante.
Raul Garcia and Nino netted for Jose Luis Mendilibar's men as they extended their unbeaten run to six matches.
Athletic Bilbao failed to win for the third consecutive game after being forced to settle for a 1-1 draw at home to lowly Sporting Gijon.
Marcelo Bielsa's side, who knocked Manchester United out of the Europa League earlier this month, saw Iker Muniain miss a penalty but still went ahead through Oscar De Marcos on 77 minutes.
Bottom-placed Sporting Gijon took an unlikely point from Estadio San Mames when Alberto Lora Ramos struck a late equaliser.
Villarreal climbed to 16th place courtesy of a 2-0 win at Rayo Vallecano, thanks to goals from Marco Ruben and Angel Lopez.
Christian Stuani's 77th-minute equaliser helped third-bottom Racing Santander draw 1-1 away to Real Betis, who had led through Roque Santa Cruz.
