Oscar Wendt got Lucien Favre's men on the way to victory in the 22nd minute and Raffael doubled their lead before half-time.
Mirko Boland's first goal of the season gave Braunschweig a glimmer of hope in the second half, but a Max Kruse penalty and a further goal from Raffael sealed victory for the Foals.
It was one-way traffic from the beginning, with visiting goalkeeper Marjan Petkovic aware that he was in for a busy night as early as the ninth minute when he fumbled Juan Arango's cross to the feat of Raffael, who scooped the ball over from close range.
Wendt opened the scoring in the 22nd minute, highlighting deficiencies in the Braunschweig defence as he cut in from the left and sent a shot into the far corner of Petkovic's goal.
Raffael had a goal ruled out for offside, but they did not have to wait too much longer for a second to arrive.
They made it look easy, with Kruse lifting the ball in for the unmarked Raffael, who headed in from five yards out.
Braunschweig reacted well early in the second half with Karim Bellarabi first denied by Marc-Andre ter Stegen before he sent in a cross for Boland to meet near the penalty spot and slide in to score.
Their hopes of a recovery were dashed in the 72nd minute when Marco Caligiuri fouled Arango inside the area and Kruse coolly slotted in the spot-kick.
Four minutes later, Kruse's shot took a deflection which meant Petkovic could only parry the ball out to Raffael, who scored his second and Gladbach's fourth, this time making no mistake from close range.
Havard Nordtveit hit a post in stoppage time, but four goals were enough for the Foals to return to winning ways, inflicting Braunschweig's fifth defeat in six games.