Carney's decisive kick was one three field goals on the day. His signing earlier in the week as a replacement for the ineffective Garrett Hartley paid immediate dividends for New Orleans (3-1).
The Saints also got 47 rushing yards from Ladell Betts on 13 carries as he subbed for the injured Pierre Thomas.
The Panthers (0-4) were led by Jimmy Clausen, who went 11-of-21 for 146 yards and a score.
DeAngelo Williams ripped off a 39-yard scoring run for Carolina, which opened the season with four straight losses for the first time since 1998.