Astana became the first Kazakh team to qualify when they netted a late equaliser to draw 1-1 at APOEL Nicosia for a 2-1 aggregate success and Leverkusen thumped visiting 10-man Lazio 3-0 on the night to go through 3-1.
Serbian midfielder Nemanja Maksimovic grabbed the crucial goal for Astana six minutes from time as Kazakhstan became the 32nd country to be represented in the group stage.
BATE of Belarus lost 2-1 at Partizan Belgrade but advanced on away goals after the tie ended 2-2, while CSKA Moscow eliminated Sporting Lisbon 4-3 on aggregate.
Rooney had not scored in almost 900 minutes before United’s trip to Belgium but brought his drought to an end when he netted his 30th Champions League goal in the 20th minute.
Running on to a neat Memphis Depay pass into the penalty area, the England international clipped the ball over onrushing goalkeeper Sinan Bolat.
It was Depay’s second assist of the tie and he also netted a double in last week’s 3-1 first-leg success.
Depay was again involved in the buildup to Rooney’s second four minutes after halftime.
The Netherlands forward found Ander Herrera in the penalty area, whose first-time pass across goal set up Rooney for a simple tap-in.
Herrera’s Spanish compatriot Juan Mata provided the assist for Rooney’s third eight minutes later, as the club captain completed his first treble in Europe since his debut against Fenerbahce in 2004.
Herrera made it 4-0 in the 63rd minute when he collected a Bastian Schweinsteiger pass and slotted home before Javier Hernandez missed from the penalty spot nine minutes from time.
“Obviously, I’m delighted to get the goals but it was a massive game for the club,” Rooney told BT Sport.
“I understand because of who I am I get publicised a lot more. But we knew we had to get into the Champions League, it was vital.”
After failing to qualify for last season’s competition for the first time since the 1995-96 season, United are through for the 20th time, equalling the record shared by holders Barcelona, 11-times winners Real Madrid and 2004 champions Porto.
Spain are the first country to have five clubs in the group stage in one season after Valencia progressed past Monaco 4-3 on aggregate despite a 2-1 defeat at the Ligue 1 side in their playoff second leg on Tuesday.
Valencia joined Barca, Real, 2014 finalists Atletico Madrid and Sevilla, who qualified as last season’s Europa League winners.
Malmo, Dinamo Zagreb, Maccabi Tel Aviv and Shakhtar Donetsk also won their playoff ties on Tuesday.
(Additional reporting by Zoran Milosavljevic in Belgrade and Ed Osmond in London, editing by Pritha Sarkar)