Eliseu scored two sublime goals as Malaga impressed against a lacklustre Anderlecht side in Belgium.
The Portuguese opened the scoring with a venomous volley on the stroke of half time.
Joaquin scored from the spot after Nacho Monreal was fouled by Cheikhou Kouyate, before Eliseu put the shine on the win with a delectable chip.
Malaga came into this, their first ever away game in the Champions League, on their longest unbeaten start to a season in a decade.
Manuel Pelligrini’s side have picked up four wins and two draws in the opening six Liga outings – and their superiority was clear again as Anderlecht struggled to keep the ball as well as their Spanish opponents.
Joaquin was dangerous throughout and he could have opened the scoring halfway through the first half when he controlled Sergio Sanchez’s cross instantly, but could only drill a low effort straight at Silvio Proto.
Anderlecht struggled to contain Malaga, who were organised and measured in their approach, and the Belgian side could have fallen behind to a free-kick routine straight off the training ground.
Feigning to shoot, Eliseu instead found Joaquin, who had peeled off the wall. His neat flick found Javier Saviola – but somehow Proto pulled of a superb save from point-blank range.
Anderlecht threatened on occasions and Dieumerci Mbokani was a handful for the Malaga defence. He could have put Anderlecht ahead when he found space in the box, but could only stab wide of the near post when the cross came in.
Instead, Malaga took a deserved lead before the break – and it was a memorable strike. Anderlecht cleared a Malaga corner as far as Eliseu, who showed magnificent technique to volley the ball straight back at goal to put Malaga ahead with the last kick of the first half.
Anderlecht started the second half strongly, but barely ten minutes in, Monreal’s driving run into the box was halted illegally by Kouyate and a penalty was awarded. Joaquin made no mistake from the spot to put daylight between the sides.
Things got worse for the home side a few minutes later when Eliseu scored a wonderful third for the visitors. Collecting Isco’s perfect through ball, the nifty forward caressed the ball over the stranded Proto.
Eliseu's strike put the game beyond doubt, but Malaga will feel as though they could have scored a few more, with Manuel Iturra responsible for a bad miss late on. But it mattered little as Malaga continue to make light work of their maiden Champions League campaign.
MAN OF THE MATCH
Eliseu (Malaga) - Two magnificent goals by the Portuguese forward. The first an unstoppable volley, the second a delicate chip.
ANDERLECHT: Proto 7, Gillet 6, Wasilewski 6, Nuytinck 6, Deschacht 6, Biglia 7, Kouyate 6, Bruno 6, Kanu 6, Jovanovic 6, Mbokani 7. Subs: Kljestan 6, Jakovenko 6.
MALAGA: Caballero 7, Sanchez 8, Demichelis 7, Weligton 7, Monreal 8, Joaquin 8, Iturra 7, Camacho 7, Eliseu 8, Saviola 7, Isco 8. Subs: Santa Cruz 6, Fernandez 6, Duda 6.