Rooney had symbolised his side's recent goal-scoring problems, which have seen them score only twice in three Premier League games, but he produced three assured finishes and Ander Herrera added another to return United to the tournament after a first season of absence in 19 years.
Louis van Gaal's side won the play-off 7-1 on aggregate on Wednesday, following last week's 3-1 victory in Manchester, and will discover the identities of their three group-stage opponents in Thursday's draw in Monaco.
"Wayne has a very strong mentality and with his level, he always shall come back."
It was Rooney's first hat-trick since a treble against Bolton Wanderers in September 2011 and his first in Europe since his dazzling debut hat-trick for United against Fenerbahce as an 18-year-old in September 2004.
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"To be honest, if I didn't have a strong character, that (the criticism) might have affected me," Rooney told BT Sport.
Van Gaal had warned his players to expect a hostile reception and there were baffled faces before kick-off at Jan Breydel Stadium when the visiting fans were subjected to a blast of 'You'll Never Walk Alone', the anthem that Club Brugge happen to share with United's bitter rivals Liverpool.
Van Gaal made two changes to his starting XI, bringing in Herrera and Michael Carrick, and the former looked less than comfortable in a midfield holding role, playing several careless passes and receiving a booking for an impetuous foul on Victor Vazquez.
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The hosts created the first chance, Luke Shaw blocking Tom De Sutter's volley, but it was United who drew first blood as Memphis Depay reprised his role of tormentor from the first leg, when he had scored twice and created an injury-time goal for Marouane Fellaini.