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Jonas Martin created Montpellier's first chance when he let fly with a right-footed effort, which flew waywardly over the crossbar.
The visitors began to mount on the pressure throughout the first half as the Reims goalkeeper did well to keep out two goal-worthy attempts from Anthony Mounier.
Montpellier grabbed the lead their play deserved just before half time when Joris Marveaux struck the ball home having been picked out adroitly by Mounier.
Cabella doubled HSC's lead straight after half time as he crashed the ball into the roof of the net from the centre of the Reims box.
The Montpellier man then doubled his tally for the night when he added the visitors' third goal of the game after being found by Mathieu Deplagne's through pass.
Reims were able to grab a goal back as Ayite finished neatly with his left, before Abdelhamid El Kaoutari turned the ball into his own net to make it 3-2.
The mini revival didn't deter Montpellier, however, as M'Baye Niang popped up in the 69th minute to add his side's fourth of the night and put the game out of sight.