The Spanish side, facing uncertainty behind the scenes amid speculation that their Qatari owner is looking to sell up, won 2-0 on aggregate to ensure a place in Thursday's draw in Monaco.
Malaga have seen Spain midfielder Santi Cazorla and Venezuela striker Salomon Rondon depart for Arsenal and Rubin Kazan respectively in what the Andalusian club has described as a process of "internal restructuring".
On Tuesday, Malaga comfortably held on in a game of few scoring chances against opponents who have taken part in the group stage nine times.
They were joined in the group stage by BATE Borisov and Dinamo Zagreb, who both qualified for the second year running, as well as last-gasp Anderlecht.
Dieudonne Mbokani and Oleksandr Yakovenko scored in the last 10 minutes to give the Belgian champions a 2-0 win over AEL Limassol, denying the Cypriot champions a chance to emulate APOEL Nicosia who reached the quarter-finals last time.
Anderlecht's 3-2 aggregate win allowed them to take what many felt to be their rightful place in the group stage for which they had originally qualified.
The Belgians were demoted to the third qualifying round after Chelsea's Champions League title last season following a sixth-place Premier League finish forced UEFA to reshuffle the places.
The changes also led to Tottenham Hotspur losing their berth and being moved into the Europa League.
BATE Borisov, full name Borisov Works of Automobile and Tractor Electric Equipment, ploughed into the group stage with a 1-1 draw at Israeli champions Hapoel Kiryat Shmona, which gave them a 3-1 aggregate win.
An early goal by Portuguese midfielder Tonel gave Dinamo Zagreb, Croatian champions for the last six seasons, a 1-0 win at Maribor in neighbouring Slovenia and sent them through 3-1 on aggregate.
