Raphael Guerreiro put the Germans in front with a missile from 16 metres before 19-year-old Jude Bellingham angled a shot into the far corner after a superb run into the box, to become the youngest captain to ever score in a Champions League match.
The England international is also the first teenage midfielder to score in three consecutive Champions League games.
Karim Adeyemi made it 3-0 on the rebound two minutes from half-time and Sevilla's Youssef En-Nesyri cut the deficit six minutes after the restart before Julian Brandt's glancing header in the 75th made sure of the three points.
Copenhagen and Sevilla, who announced the departure of coach Julen Lopetegui minutes after the game, are on one point. The coach had been in charge since 2019.
"That was definitely the reaction we wanted to show. I think the difference between today and the other day [against Cologne] is that we did our work early," Bellingham said.
"Three goals in the first half allows you to be a bit more comfortable in the second. I think that's a lesson for us going forward.
"For a start, the defenders and [keeper] Alex [Meyer] were absolutely brilliant tonight. I got this Player of the Match award for the goal and the assist, but I think those guys at the back were a different level."
Sevilla, struggling in 17th place in La Liga, missed several early chances through En-Nesyri and they were punished when Guerreiro struck with a superb shot.
The hosts, who have won just one of their 10 matches this season, had a golden double opportunity to level but Dortmund keeper Alexander Meyer pulled off a sensational save to thwart En-Nesyri's header.
Jose Angel Carmona fired over the bar from the resulting corner and it was Dortmund who scored again -- twice in three minutes -- through Bellingham and Adeyemi to leave Sevilla with a mountain to climb even after En-Nesyri's goal in the 51st minute.
Sevilla's pressure gradually eased off as the hosts ran out of steam and Dortmund found more space to attack. They got their fourth goal when Youssoufa Moukoko chipped the ball into the box for Brandt to head in.
As Dortmund players celebrated their win, the outgoing Lopetegui left the pitch waving as the fans chanted his name.