The result extended Leverkusen's winning run in the Europa League group stage and League Phase to seven matches, while giving new head coach Carles Martinez another positive result as he settles into the job.
Leverkusen dominated the opening stages and created several opportunities before finally breaking the deadlock.
Martin Terrier went close with a long-range effort that struck the post, while Edmond Tapsoba saw a close-range header kept out by Celje goalkeeper Zan-Luk Leban.
The breakthrough eventually arrived in fortunate fashion. Aleix Garcia sent a low cross into the area, but it lacked enough pace to cause a major threat. Celje defender Svit Seslar attempted to clear, only to send the ball into his own net.
Leverkusen continued to press for a second goal, with Garcia particularly influential in midfield and forcing Leban into several saves.
Celje had their moments before the break, however, with Mark Flekken producing an excellent stop to deny Seslar. The Leverkusen goalkeeper had already made a vital double save to keep out Benjamin Verbic as the visitors threatened on the counter-attack.
Leverkusen remained in control after the interval and Leban was again called into action, this time denying Facundo Medina's header.
The Celje goalkeeper then produced another important save when he pushed Afonso Moreira's long-range effort onto the crossbar.
But Celje could not prevent Leverkusen from doubling their advantage moments later.
From the resulting corner, Medina met the ball with a powerful volley and found the net to put the German side firmly in control.
The second goal ended Celje's hopes of taking anything from the match as Leverkusen comfortably managed the closing stages.
Leverkusen have now gone three matches unbeaten under Martinez, scoring at least twice in each game. Celje, meanwhile, have won only one of their last seven matches as they continue to struggle for the form that helped them win the Slovenian title last season.