Nuno Espirito Santo rested Jota at Molineux on Friday (AEDT) with Wolves already qualified and facing a home game against top-six rivals Tottenham in the Premier League at the weekend.
However, after his 56th-minute introduction, Jota netted three times in quick succession as the hosts cut loose.
Leander Dendoncker was also on target but, after finishing second behind Braga, Nuno's side will not be seeded for Monday's last-32 draw, meaning they could face Ajax or Inter, who have dropped into the tournament via the Champions League.
Wolves thought they had scored in the 18th minute but Patrick Cutrone had strayed offside from Ruben Vinagre's pass, with a wayward Ruben Neves drive summing up a first half devoid of quality.
Jota's arrival changed everything for the hosts, though. The forward nodded home after superb work on the right wing by Pedro Neto, while his second came just six minutes later.
Dendoncker had hit the woodwork when facing an open net but, when he then unleashed a 25-yard drive, goalkeeper Utku Yuvakuran turned it on to the post and Jota converted the rebound.
Besiktas had already been eliminated and it was struggling to cope with a suddenly rampant Wolves, Dendoncker nodding in Joao Moutinho's corner.
Oskar Buur set up Jota to clinch the match ball from close range and teenage debutant Owen Otasowie almost added a fifth, hitting the crossbar.