Jordan Hill had a double-double for the Rockets off the bench with 12 points and 12 rebounds.
The Rockets (3-6) broke open a tight game in the third quarter and the poor-shooting Bobcats could never put together a big run.
They did manage to cut the lead to five with 2:30 left, but Parsons made a 3-pointer from the right wing and a jumper from deep in the left corner to put the Rockets back up by double digits.
The Rockets held the Bobcats to 35 percent shooting from the field and outrebounded them 57-44.
The Rockets only shot 39 percent from the field, but it was good enough for the win.
Parsons came into the game averaging just 5.3 points this season but got hot early, scoring six of his team's first eight points.
He shot 9 of 16 from the field and added seven rebounds to give the Rockets a much-needed spark.
The Rockets began the season 2-2, but had lost four in a row while struggling on offense.
The Bobcats (2-8) couldn't muster much offense with the exception of center Byron Mullens, who scored 15 points and had 10 rebounds off the bench. It was the sixth time in eight games Mullens has finished in double digits in scoring and was his second double-double of the season.
The Bobcats were playing without starting forwards Corey Maggette, who is out two to four weeks with a strained left hamstring and Tyrus Thomas, who needed a break to rest his legs after seeing significant playing time in the team's previous three games.
Their other top scorers didn't pick up the slack.
Boris Diaw, who had 19 points and 10 rebounds the night before against the Knicks, was held to four points on 2 of 13 shooting.
D.J. Augustin came into the game averaging 18.6 points, 7.8 assists and 5.4 rebounds in his previous five games, was held to 11 points on 4 of 13 shooting.