Bellingham silenced the boisterous crowd in Istanbul with the opening goal and then unpicked the home defence to serve up a simple tap-in for Haaland to claim his 21st Champions League goal just before half-time.
Javi Montero headed in a consolation goal for Besiktas deep in added time.
Haaland underlined his reputation as a prolific scorer, taking his tally to 14 goals in 10 games this season for Dortmund and Norway.
Dortmund’s duo of Haaland and Bellingham bumped chests to celebrate the second goal.
However, the club reportedly faces a fight to keep both young stars past this season with Europe’s elite tracking the pair.
Haaland, 21, has now scored 66 goals in 66 games for Dortmund.
His contract has a release clause, which becomes active next year, that could see him leave for 75 million euros ($88 million).
Likewise, a host of Premier League clubs such as Manchester City, Liverpool and Chelsea are chasing Bellingham, who was outstanding in Istanbul.
Only a one-handed save by Dortmund goalkeeper Gregor Kobel after six minutes denied Besiktas striker Michy Batshuayi, who is on loan from Chelsea.
Yet it was one-way traffic for the rest of the first half.
The Besiktas crowd was hushed when Bellingham latched onto Thomas Meunier’s cushioned volley in behind the defence and fired between the legs of Besiktas goalkeeper Ersin Destanoglu.
Dortmund doubled the lead just before half-time when Haaland tapped in after Bellingham’s mazy run.
The Besiktas team made a point of applauding their vocal supporters before trudging off 2-0 down at the break.
The hosts raised their game as Besiktas playmaker Miralem Pjanic caused the Dortmund defence plenty of problems.
At the other end, only good saves from Destanoglu denied further goals by Bellingham, who came off for the last 20 minutes, and Haaland.
Haaland gave a wry smile as he walked off to a chorus of whistles by home fans when he was substituted with five minutes left.
Dortmund were denied their first clean sheet in over five weeks when Montero got on the end of a Pjanic free-kick in stoppage time.