The Nuggets soared to a 17-point halftime lead and easily held on thanks in large part to Fournier's effort off the bench.
He received extra playing time with Tim Lawson out of the lineup suffering from a heel injury. Fournier hit 6-of-9 from the field and was one of three bench players to reach double figures.
The Nuggets have not lost at home since Jan. 18, when they suffered a four-point defeat at the hands of Washington.
Deron Williams scored 19 points to lead Brooklyn, which is 4-2 on an eight-game road trip.
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