Juan Arango was joined by fellow forwards Raffael, Max Kruse and Patrick Herrmann on the scoresheet as Lucien Favre's attack-minded tactics yielded the desired result.
Only an own goal from Havard Nordtveit gave Bremen a glimmer of hope at 2-1, but it was an otherwise one-sided game in Monchengladbach.
Gladbach started well with a few early sighters placed wide of Sebastian Mielitz's goal.
Aaron Hunt then tried to beat Marc-Andre ter Stegen with a speculative effort from the halfway line, but that was the closest they were allowed to the Gladbach goal.
The home side's efforts were rewarded in the 36th minute when Granit Xhaka played the ball just where Arango wanted it - in front of his left foot.
The Venezuelan did the rest, sweeping the ball low through the legs of Mielitz to break the deadlock 10 minutes before half-time.
Gladbach's second came less than 10 minutes into the second half when Tony Jantschke's effort was spilled out by Mielitz to the awaiting Raffael, who doubled the hosts' advantage.
It was a costly mistake from Mielitz, who only moments earlier had been at full stretch to turn Raffael's angled shot wide.
Gladbach started to dominate, but they were made to sweat when Nordtveit headed a free-kick into his own net in the 69th minute.
Five minutes later, Kruse restored the home team's two-goal cushion, finishing off an excellent team move with a composed left-footed finish.
Herrmann then sealed the win and ensured that all four of Gladbach's forwards got a goal as he burst through, dribbled past Mielitz and stroked the ball into an unguarded goal.