Malaga's success is all the more laudable considering the upheaval they went through in the close season when media reports said the club's Qatari owner wanted to quit after two years in charge, there was a fire sale of top players and wages were delayed.
The Group C leaders have 10 points from four matches and are five ahead of second-placed Milan. In Tuesday's other game, Anderlecht (four points) beat Zenit St Petersburg (three) 1-0.
"It's a great achievement to qualify with two games to spare especially doing it in such a difficult stadium as this one," Pellegrini told reporters.
The only negative on a night of celebration for unbeaten Malaga was that they conceded their first goal in the competition.
Milan kept their qualifying hopes intact thanks to injury-plagued Alexandre Pato's first goal in 11 months. His second-half equaliser cancelled out Eliseu's effort five minutes before halftime.
The Italians, who also spent the close season offloading their leading players, produced another shoddy performance in front of a restless and half-empty San Siro stadium.
Malaga goalkeeper Willy Caballero had kept clean sheets in two games in the qualifying rounds, three in the group and for another 73 minutes on Tuesday before he was finally beaten by Pato's header.
The 23-year-old forward, once considered one of Brazil's most promising players, has seen his career stutter amid a series of nagging and hugely frustrating muscular injuries and was starting only his second match of the season.
Pato produced a subdued performance, showing flashes of inspiration, before rising to meet Kevin Constant's long cross at the far post.
SIGNS OF LIFE
Milan had shown signs of life by taking seven points from their last nine in Serie A but their efforts on Tuesday tested the patience of the 30,000 crowd who jeered coach Massimiliano Allegri when he replaced Stephan El Shaaraway with Kevin-Prince Boateng in the second half.
"I think the way things are going the decisive match will be the last one [at home to Zenit]," said Allegri.
"We played well. In the first half we created a number of chances and in the second we had them on the ropes."
Milan got on top midway through the first half with Bojan Krkic at the centre of the action.
The Spaniard skipped past two defenders and saw his shot beaten away by Willy and then set up El Shaaraway for a goalbound shot that was deflected away by a defender.
The Argentine goalkeeper then produced an outstanding save as he dived backwards to turn Urby Emanuelson's curling free-kick past the far post.
Milan were otherwise lacklustre and Malaga's goal came after they lost possession from a throw.
The ball ended up with Isco who threaded his pass between three defenders for Eliseu to score.
There were few chances for either side in a scrappy second half until Pato ended his drought.
Milan dominated the final stages but the best they could manage was a Boateng volley saved by Willy.
