Orlando had lost four of its last five and was coming off the embarrassment of surrendering an NBA season-high 60 points to Philadelphia's Allen Iverson the night before.
The Hornets should've been a breather -- but the Magic know better after losing to cellar-dwellers Atlanta and Golden State in the last two weeks.
"Even the worst teams, they have a leading scorer," Orlando coach Johnny Davis said. "But what you want to do is make the game difficult for them, and we haven't done that lately."
Orlando trailed by 11 points midway through the first quarter and nearly blew a seven-point lead in the closing minutes. But no one on the Magic was concerned with aesthetics.
"It would be good to get a blowout victory, of course," said Francis, who scored nine points in the final 4:44. "But we'll take a win any way we can get it."
After Francis' free throws put the Magic ahead 93-86, the Hornets cut the deficit to a point on Dan Dickau's layup with 15.9 seconds remaining.
Dickau scored a career-high 28 points, 17 in the second half. He hit seven 3-pointers, four in the third quarter when he was all that stood between the Magic and a rout.
"After Iverson scored 60 (Saturday) night, I'm sure they talked about defense more than normal," said Dickau, who shot 10-of-16. "It was just normal flow-of-the-game shots I was making."
Dickau fouled out four seconds later, and Francis hit two free throws to re-establish a three-point lead. Francis made all five of his foul shots in the fourth quarter, shooting 10-for-11 for the game.
Francis also had 10 assists.
The Hornets' bid to tie fell short, with J.R. Smith's 3-pointer missing everything. Smith had 20 points.
"If you look at our schedule, we've had so many close games that we lost," Dickau said. "We could easily have 20, 22 wins right now, and that's the frustrating thing. But we didn't get it done in those games, so there's no need saying we could've."
For Orlando, Garrity added 12 points, and Grant Hill and Dwight Howard each had 11. Howard also had 10 rebounds for his 17th double-double.
Early on, not even the lingering sting from Iverson's performance could rouse the Magic.
Orlando began the night late on rotations, lost in transition and sloppy on offense. Francis' wild pass, cashed in for Dickau's fast-break jumper, capped off a 16-2 run that put New Orleans ahead 20-9.
It was the Magic's reserves that finally put a charge into the team. Rallying to a 33-28 lead, Garrity scored 10 points, while Turkoglu and DeShawn Stevenson each added six.
At halftime, the game was tied at 49.
Hornets forward Lee Nailon missed his sixth straight game with a sore left groin. ... P.J. Brown sprained his left ankle late in the second quarter, and didn't play in the second half. ...
Bostjan Nachbar had his streak of consecutive 3-pointers made end at eight, when he missed his first try. The team record is nine straight, set by Bryce Drew in 2001-02.