A Wayne Rooney hat-trick fired Manchester United back into the group stage of the Champions League with a 4-0 win, 7-1 on aggregate, in their play-off second leg at Club Brugge on Wednesday as Lazio crashed 3-0 at Bayer Leverkusen, 3-1 on aggregate.
Rooney's treble was also a timely return to form for the England striker, who had gone 10 games without a goal for United prior to Wednesday.
United - who missed out on Champions League football last season - will discover their group opponents in Thursday's draw in Monaco.
In Germany, Lazio had gone to Bayer Leverkusen hoping to defend a one-goal advantage and reach the main draw for the first time since the 2007/08 season.
But the Italians were trailing following goals from Hakan Calhanoglu (40) and Admir Mehmedi (48) and faced an uphill battle as they played the last 20 minutes with ten men when Brazilian Maurício was sent off for a second yellow card.
Karim Bellarabi put the result beyond any doubt for the Germans when he finished into an empty net two minutes from time after good work from Julian Brandt.
Astana made history as they became the first Kazakh team to qualify for the main competition with a 1-1 draw at Cypriot side Apoel in a 2-1 aggregate victory.
The Kazakh club had taken a 1-0 lead to the Cypriot capital Nicosia for their second leg against 2012 quarter-finalists APOEL.
Semir Stilic's superb free-kick put the Cypriots ahead after 60 minutes but six minutes from time Nemanja Maksimovic tapped in the winner from close range.
In Serbia, Belarussian champions BATE Borisov reached the group stages for the fourth time in five years on away goals after a 2-1 loss at Partizan Belgrade, having won the first leg 1-0.
Igor Stasevich put BATE ahead after 25 minutes after the ball bounced into his path, only for Partizan to level after 74 minutes via an own goal from BATE's Maksim Zhavnerchik.
An injury-time Ivan Saponjic goal proved academic in the end as Partizan earned a hollow victory on the night.
2010 quarter-finalists CSKA Moscow also advanced after a come-from-behind 3-1 success against Sporting Lisbon -- 4-3 on aggregate -- to add to their record of seven wins out of seven in Russia this season.
Portuguese giants Sporting had taken a 2-1 advantage to Moscow and Teofilo Gutierrez scored an away goal after 36 minutes before a second half double from CSKA's Ivorian striker Seydou Doumbia on 49 and 72 minutes left the tie level.
Nigerian striker Ahmed Musa got the winner for the Russians five minutes from time as they qualify for the main draw for the third straight season.
On a superb night for Louis Van Gaal's Manchester United in Belgium, Dutch midfielder Memphis Depay had a role in Rooney's first two goals on 20 and 49 minutes, with a Juan Mata cross eight minutes later allowing the United captain complete his hat-trick.
Spaniard Ander Herrera compounded a night of misery for the Belgian club after 63 minutes following a Bastian Schweinsteiger cross to put the three-time winners of the Champions League through in style.
Manchester United - winners in 1968, 1999 and 2008 - didn't feature in the competition last season but had previously reached the group stages for 18 years in succession.
Brugge, meanwhile, hasn't made the group stages since the 2005/06 season when it finished third in Group A behind Juventus and Bayern Munich.