Hazell received a red card midway through the second period after he aimed a flurry of punches at an opponent on the floor and used his knee. Hazell's back-row colleague Matt Cox was sin-binned for an off-the-ball challenge in the same incident that meant Gloucester were temporarily reduced to 13 men.
But the Aviva Premiership club prevailed thanks to wing Ian Clark's 30th-minute try, while Tim Taylor and Billy Twelvetrees booted second-half penalties.
Full-back Jean Baptiste Claverie kicked two penalties for the home side, yet Gloucester deserved their Pool One triumph that sets them up for next Thursday's Kingsholm appointment with Bordeaux-Begles.
Mont-de-Marsan, bottom of the French Top 14, did not help themselves as their former Scotland international lock Scott Murray and substitute hooker Ephraim Taukafa collected yellow cards in each half.
And with torrential rain making handling a hazard for both teams, Gloucester will be relieved to head home with four Pool One points in the bag.
Wing Charlie Sharples looked lively on his first game back after four weeks' sidelined recovering from shoulder trouble, while Gloucester skipper Mike Tindall also showed some neat touches.
But Gloucester's star performers proved to be the young and inexperienced front-row unit of Yann Thomas, Koree Britton and Shaun Knight, who dominated the scrums throughout.