Newton guided the Panthers on a five-play, 65-yard driving in the closing seconds and capped it with a pass into the front of the end zone that Hixon dove to reel in for the game-winning TD.
Newton finished with 181 yards and one interception on 13-of-22 efficiency for surging Carolina (11-4), which notched a 10th win in 11 contests to clinch its first playoff berth since 2008.
The Panthers also moved one game ahead of the Saints for first place in the NFC South with one game remaining. A win over Atlanta next week would give them the division title and the NFC's No. 2 seed.
DeAngelo Williams scored on a 43-yard touchdown run in the second quarter.
On defense, Luke Kuechly compiled a team-record 24 tackles to go along with an interception.
Drew Brees completed 30-of-44 passes for 281 yards but was picked off twice and managed only one TD for New Orleans (10-5), which was still waiting to clinch a post-season berth.