Parsons was good on all seven of his field goal attempts and finished with 21 points, one of six Houston players to reach double figures.
Houston led by 17 during the opening quarter and the struggling Nets could not fight back.
Omri Casspi had 16 points and Aaron Brooks pitched in 14 for the Rockets, who made 19-of-32 shots from beyond the arc.
Houston has won four in a row while Brooklyn has lost seven out of eight.
Brook Lopez returned to the Brooklyn lineup after missing seven games with an ankle injury. Lopez and Miles Plumlee each scored 16 points.