
Bremen were dominant against the hapless hosts, taking a two-goal lead at half-time thanks to goals from Samuel Mbangula and Jens Stage.
Romano Schmid added a second-half penalty and Boniface, signed on a season-long loan from Bayer Leverkusen, came off the bench with 75 minutes played.
The Nigerian threaded a brilliant pass through a crowded penalty box, allowing Njinmah to score as Bremen won their first match of the campaign.
Gladbach are still yet to score this season in three matches.
Earlier on Sunday, St Pauli came from a goal down to beat Augsburg 2-1, with Burnley loanee Andreas Hountondji scoring for the third straight match.