Florian Wirtz debuted for Leverkusen at 17 years old, surpassing the previous record held at the club by Kai Havertz. Meanwhile, Nuri Sahin started on the bench for the hosts.
After constant pressure, Leverkusen grabbed the lead when Havertz headed past Jiri Pavlenka after a cross assist from the far post by Moussa Diaby following the 28th minute.
The lead lasted just two minutes as Bremen drew level thanks to Theodor Gebre Selassie who finished off a delivery from Leonardo Bittencourt.
Havertz however pulled the away side back ahead with another clinical header from the centre of the six-yard area following a delicate cross from Kerem Demirbay on 33 minutes.
Philip Bargfrede almost made it three on the brink of halftime, but his header from Bittencourt's ball rose high and wide of goal.
The second half began more cautiously as neither outfit opted to go on the front foot, although Bremen's Bargfrede did make way for Johannes Eggestein on 54 minutes.
Bremen came into the match on a run of nine defeats in their last 11 league matches with relegation hanging over their heads.
This was compounded on 61 minutes as Mitchell Weiser headed into the bottom left corner to give the visitors a third goal following a well-weighted cross from Diaby.
A solid through ball from Karim Bellarbi in the final 12 minutes found Demirbay, who made no mistake with a solid right-footed strike to complete an emphatic showing on the night.
The result sees Leverkusen in fifth place, boosting their European chances whilst Bremen drop deeper in the relegation zone.