The win lifted the Foals to fourth, three points behind their opponents, who are third, and ahead of Bayer Leverkusen on goal difference.
The rout began in the 14th minute when Hertha goalkeeper Rune Jarstein's poor clearance was intercepted by Mahmoud Dahoud who played the ball to Hazard and the Belgian did the rest.
Jarstein partially atoned for his earlier blunder, keeping Hertha in the game with some fine saves as the hosts dominated.
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But Hertha caved in after Andre Hahn, standing in for Gladbach's injured leading scorer Raffael, scored with a shot on the turn on the hour.
Patrick Hermann fired home the third in the 76th minute, Hazard, the younger brother of Chelsea and Belgium winger Eden, added the fourth and Ibrahima Traore scored from a tight angle to complete the rout.
The top three teams in the Bundesliga qualify directly for the Champions League group stage and the fourth-placed side goes into the final qualifying round.
(Writing by Brian Homewood; Editing by Ken Ferris)
