Romelu Lukaku scored two goals to reach a total of five in the tie as Everton cruised past Young Boys to progress to the Europa League last 16.
The Belgian striker followed up his hat-trick in the 4-1 win in Switzerland with two more after Sekou Sanogo had given the visitors the lead.
Kevin Mirallas then made it 3-1 before the break as Everton ensured a safe passage into Friday’s last-16 draw.
They are now the only British side remaining in the Europa League.
The Merseysiders are flying the flag after Liverpool, Tottenham and Celtic all exited the competition on Thursday.
A similar fate was never likely to befall Roberto Martinez’s side after their exploits in Bern last week but a slow start to this encounter gave Young Boys a glimmer of hope and left the Goodison Park crowd frustrated.