The England international scored one goal and set up another in a comfortable win for the Bundesliga side, who also saw Julian Brandt, Karim Adeyemi and Raphael Guerreiro strike at the Estadio Ramon Sanchez Pizjuan, while Youssef En-Nesyri pulled one back for the hosts.
A wave of early pressure from Edin Terzic's side paid off with just seven minutes on the clock, as left-back Guerreiro received a cross-field ball from Bellingham before cutting inside and firing home a thunderous strike into the far corner.
Dortmund immediately found themselves on the back foot after and had to rely on Alexander Meyer to make two saves in quick succession from En-Nesyri, but the Sevilla attacker was then handed a reprieve as he received a red card for a last-man foul on Salih Ozcan before VAR overturned the decision due to a previous foul on Jesus Navas by Adeyemi.
After riding a wave of pressure from Los Palanganas, Dortmund eventually doubled their lead through their record-breaking skipper. In the 41st minute, Bellingham produced a stunning solo run and finish into the far corner, becoming the youngest-ever player to score a goal in the Champions League as captain at 19 years and 98 days.
Only a couple of minutes later, it was three for the dominant Black and Yellows, as Adeyemi was the quickest to reach and fire home after Bono had saved from Youssoufa Moukoko.
Things were looking bleak for the Spanish side, but En-Nesyri finally took one of his chances in the 51st minute - heading home from a corner to hand Sevilla a glimmer of hope.
However, Brandt would put the cherry on the icing on the cake for Dortmund, meeting Moukoko's cross with a header towards the back stick to restore the visitors' three-goal cushion.
There was time for Kasper Dolberg to rattle the woodwork with an acrobatic effort, but Dortmund were otherwise untroubled en route to a straightforward win to pile even more pressure on the under-fire Julen Lopetegui.
Dortmund remain second in the section on six points - three behind perfect Manchester City - while Sevilla are still on one point but have now risen above Copenhagen into third place on goal difference after the Danish side were thrashed 5-0 by the Premier League champions.
The two sides will renew hostilities in six days' time at the Westfalenstadion, where Dortmund will endeavour to seal qualification for the last-16 at the expense of Sevilla's chances of a top-two finish.