Mickael Pietrus had 19 points for Orlando (5-0) and teammate Vince Carter scored 13 of his 18 points in the first quarter in the game played at Wichita State's Koch Arena.
David West led New Orleans (1-3) with 14 points while Chris Paul added 13.
The Hornets cut into a 26-point halftime deficit as West scored six points in a 9-0 run that brought them within 69-52.
That's when Anderson took over, hitting four 3-pointers and scoring 16 points in a 3 ½-minute stretch that pushed the Magic's lead back to 87-57.
Anderson, who came to the Magic in the trade that brought Carter from the New Jersey Nets, finished 6 of 9 from 3-point range.
"That was fun," Anderson said. "It's always fun when you're feeling it, but when the guys got me open and the crowd got into it, it was great."
The Magic shot 60.9 percent from the field and 63.3 percent from the 3-point line. Orlando's biggest lead was 104-64 on a 3 by Carter early in the fourth quarter.
"People keep calling [Anderson] the other guy in the Vince Carter trade," Orlando coach Stan Van Gundy said, "and when I told you guys [in the media] he was a big part of the thing, you rolled your eyes. But he fits the way we play. Our team is built inside out, and you can't leave him open."
Led by Carter going 4 of 6 from the 3-point line, Orlando took control of the game with its long-range shooting in the first half. The Magic were 9 of 13 on 3s in the first half, while New Orleans was 3 of 10. That helped Orlando twice build its lead to 30 points in the first half.
"He's getting more and more comfortable," Van Gundy said of Carter.
Paul scored four points, all from the free-throw line, in nearly 15 first-half minutes.
"We've got to get better defensively," New Orleans coach Byron Scott said. "Communication is the key."