OM were able to secure all three points on the road, thanks to a last-minute finish from Dimitri Payet, who netted a 20-yard effort.
"I was very happy with our first half, which was better than we've produced for quite a while, with a lot of movement, simplicity, enjoyment and desire to go after the three points," Anigo said after the game.
"Every time Montpellier equalised, our desire for the win came to the fore. We controlled the match and I think it was a deserved win.
"Mathieu Valbuena was playing at international level tonight; it changes everything when he is available and moving all the time. But we had several players who lifted their game tonight."
The win sees Marseille sitting in sixth position in the Ligue 1 table.