Anderlecht and Valencia were joined by Lille, who beat Slavia Prague 3-1, and former England coach Steve McClaren's Twente Enschede, who completed the lineup for the last 32 with a 1-1 draw at eliminated Steaua Bucharest.
Only four places were up for grabs in Thursday's 12 games, with a number of teams having already qualified including Anderlecht's opponents Ajax.
Anderlecht, former winners of the old UEFA Cup, broke through after 13 minutes when Mbark Boussoufa floated in a free kick and Lukaku rose to head his first European goal.
The teenager was on target again nine minutes later with another header after a pinpoint cross from Jonathan Legear.
Legear helped himself to the third before halftime, poking in the rebound after keeper Maarten Stekelenburg fumbled Boussoufa's low centre.
Urby Emanuelson pulled one back for four-times European champions Ajax midway through the second half.
SALZBURG WIN
Anderlecht and Ajax finished level on 11 points in Group A, the Belgians edging top spot on head-to-head record.
Valencia scored in stoppage time at the end of each half to beat Genoa and top Group B with 12 points.
Bruno Saltor was on target with a looping header at the end of the first half for the Spaniards before former Argentina forward Hernan Crespo revived Genoa with a superbly-taken goal six minutes after the break.
Villa wasted a chance to put Valencia back in front when he fired wide from the spot but atoned by capitalising on keeper Alessio Scarpi's poor clearance to snatch the winner in the fifth minute of stoppage time.
Goals from Yohan Cabaye, Gervinho and Ludovic Obraniak gave Lille a 3-1 win over Group B bottom club Slavia Prague.
Twente finished second in Group H, behind winners Fenerbahce, when Ronnie Stam scored with a long-range shot which deflected past Robinson Zapata in the 35th minute to cancel out an earlier goal for Steaua by Pantelis Kapetanos.
Salzburg were the only team to complete the group stage with a 100 percent record, winning 1-0 at Villarreal thanks to a seventh-minute goal by Dusan Svento in Group G.
Both teams had already qualified.
