The visitors had completely dominated the opening period but had to wait until first-half stoppage time to break the deadlock as Eliseu seized on a loose ball on the edge of the area and cannoned a volley into the top corner.
Joaquin then made the game safe from the spot after Nacho Monreal had been clipped by Cheikhou Kouyate inside the area and Eliseu rounded off a perfect night for Manuel Pellegrini's side as he raced onto Isco's pass and coolly chipped the ball over Silvio Proto.
Both sides had enjoyed positive results on matchday one as Malaga thrashed Zenit St Petersburg 3-0 on their Champions League bow whilst Anderlecht had taken a point away at AC Milan, but it was the Spanish side who showed they have the class to progress further in the competition as their passing and movement proved far too good for the Belgian champions.
Joaquin was twice denied by smart saves from Proto in the opening quarter before Martin Demichelis really ought to have put the visitors in front when he headed Joaquin's corner wide from close range.
Proto then made a world-class save to deny Javier Saviola the finishing touch to what would have been a wonderful team goal as Eliseu played a free-kick short to Isco and his backheel freed to Argentinian inside the area but Proto got a strong left hand to his poked finish to turn the ball over the bar.
Joaquin was then denied a certain goal again, this time by a brave block from Olivier Deschacht on the stroke of half-time, but when the resulting corner was only cleared to the edge of the area Eliseu was waiting to send a rocket of a shot into the top corner.
Anderlecht started the second period in a more positive manner and had their first shot on target when Sacha Kljestan fired straight at Willy Caballero a minute after the break, but any hope they had of a comeback disappeared on 55 minutes when Kouyate unnecessarily dived in on Monreal and Joaquin gave Proto no chance from the spot.
And with the hosts having to push forward in search of a way back into the game Malaga exposed the space in behind their defence to score the third just after the hour as Isco released Eliseu and he showed how high his confidence is at the moment as he flicked the ball over Proto and into the far corner.
Manuel Iturra should then have added his first Malaga goal as he exchanged passes with Isco but the Chilean's weak effort was straight at Proto.
However, it matter little as Malaga saw the game out comfortably to take their place at the top of Group C.