Zenit St Petersburg's 1-0 victory at AC Milan, who clinched second place last month, sent the Russians into the Europa League in third spot with seven points, one behind the Italians and two ahead of the Belgian side.
Unbeaten Malaga, making their debut in Europe's elite club competition, topped the group on 12 points.
Local media reported trouble between Anderlecht supporters and Spanish police outside the ground before kick-off and television footage showed baton-wielding officers fighting with fans in the Rosaleda stands at half-time.
Malaga captain Duda had put the home side ahead with a fine curling effort just before the break but Milan Jovanovic's deft chip made it 1-1 five minutes into the second half.
Duda put Malaga back in front when he took down a floated Diego Buonanotte pass in the 61st and drove the ball past keeper Silvio Proto before Dieudonne Mbokani made it 2-2 in the 89th.
The visitors pressed for a winner, which would not have been enough to secure third spot because their goal difference would still have been sorse than Zenit's, but Carlos Kameni pulled off another excellent save to deny Mbokani in added time.
"They had chances but Kameni made some good stops," Malaga coach Manuel Pellegrino, whose side have been struggling in La Liga in recent weeks, told a news conference.
"It was an entertaining game for the fans but the goal is achieved and we'll see now how many points we'll have in La Liga at the end of the year," he added with his side lying fifth in the domestic standings on 22 points from 14 games.
REACTION SAVES
As expected Pellegrini fielded a second-string side, with Kameni in goal for Willy Caballero, Roque Santa Cruz leading the line and winger Joaquin and playmaker Isco rested.
Both sides had chances in an entertaining first half, Manuel Iturra, Diego Buonanotte and Weligton going close for Malaga and Kameni pulling off splendid reaction saves to deny Dieudonne Mbokani and Massimo Bruno.
Anderlecht had not won on the road in the Champions League since a 1-0 success at Malaga's La Liga rivals Real Betis in the 2005/06 group stage.
They needed a big win to have any hope of going through to the Europa League but ultimately lacked the firepower against a well-drilled defence.
"We have played against a great team," Anderlecht midfielder Lucas Biglia said on www.uefa.com.
"We knew that it would be tough, but we wanted to complete a good Champions League," added the Argentine. "Malaga have great players and tonight they showed it."
Qatar-owned Malaga have made it through to the last 16 as group winners despite a turbulent summer disrupted by rumours that owner Sheikh Abdullah Bin Nassar Al Thani was planning to sell up and the transfer of some of their best players.
The club, which still faces punishment from UEFA for overdue payments to creditors, missed out on a one million euro bonus they would have earned for a win on Tuesday.
Howeve
