Parsons said the next step in their playoff chase is improving defensively.
"We can score on anybody," he said. "We've got to put all our effort, all our energy and the defensive end. We've got to be able to win games when we don't score 100 points."
Harden (knee) and Jeremy Lin (ankle) were both game-time decisions Friday after sitting out the Rockets' practice on Thursday. Both started as scheduled, though, and were needed to keep up with an inspired Magic team offensively.
The Rockets shot 60 percent (24 for 40) in a fast-paced first half, including 11 3-pointers. But Orlando was just as strong at 55 percent (24 for 43) and trailed just 64-61 at halftime.
Parsons had 15 first-half points to lead the Rockets, with Nicholson and Harris each scoring 13 for the Magic.
Orlando also shared the ball with 20 assists and took care of the ball with only four turnovers.
That changed in the closing minutes, a recurring theme that Magic coach Jacque Vaughn also was high on the effort of Houston's Beverley.
"I think he came into the game and finished the stretch run for them," Vaughn said. "He hit key shots for them and, at the same time, was able to apply a little defensive pressure. I give a lot of credit to him and the fact that they were able to turn up the defense a little bit on us."
The Rockets return home to host Dallas on Sunday, hoping to keep their momentum alive.
Coach Kevin McHale said while it was nice to breakthrough with a victory, they still aren't playing like a team that is playoff bound by his standards.
"We don't have a great rhythm right now," he said. "We've been a team that's kind of start and stop...You already know we've got to hit the start button here again and get some rhythm going. If we can get a couple wins, get our practice in tomorrow and (can) hopefully start something good."
NOTES: Moore had a career-high 11 assists. ... Magic PG Jameer Nelson missed his fifth straight game with a left patella tendon contusion. He remains day-to-day. ... Former world champion boxer Roy Jones Jr. sat courtside.
Follow Kyle Hightower on Twitter at http://www.twitter.com/khightower.