Morris Peterson made a 3-pointer with 3:23 left to give the Hornets (2-1) the lead for good at 105-102.
Shawn Marion scored 18 points and grabbed 20 rebounds in 29 minutes, sitting out the fourth quarter along with the other Suns regulars.
Chandler added nine rebounds in 24 minutes for New Orleans, which used some of its starters until the end.
Sean Marks and Marcus Banks, who helped spark a late fourth-quarter rally, each had 14 points for Phoenix (1-1).
Rasual Butler added 13 points for the Hornets, while David West was held to 2-of-12 shooting and finished with six points and seven rebounds.
Chris Paul scored seven straight points to give the Hornets the lead midway through the third quarter, and Peja Stojakovic hit back-to-back 3-pointers to help New Orleans opened a double-digit advantage.
But Boris Diaw and Raja Bell hit back-to-back shots to cut the Hornets' lead to 96-91 with 7:35 left, and second-round pick D.J. Strawberry made a layup and a 3-pointer to get Phoenix within 100-99 with 5:41 remaining. Banks hit a 3-pointer with 4:33 left to give Phoenix a 102-100 lead.
Steve Nash added 13 points and 11 assists, 10 in the first half to help Phoenix keep it close.
New Orleans had opened up a 20-point first-half lead, sparked by free-agent acquisition Melvin Ely, who scored 10 points in the second quarter. But Phoenix took advantage of a Hornets cold spell to cut the lead to 57-54 at the break.
New Orleans missed 14 of its last 15 shots of the second quarter after leading 51-31 with 8:30 left in that period.
Ely was listed as being out with a viral infection. He had sat out the Hornets' first two games.
Phoenix offseason pickup Grant Hill missed seven of his first nine shots and finished 4-of-11 for 12 points. Bell added 14 points.