Clinging to a 2-1 lead in the third period, and with the Flames playing their most inspired hockey of the game, Arnott's second goal of the night proved fatal for Calgary.
Kiprusoff, who had been spectacular all night in goal for the Flames, had no chance on Shea Weber's shot from the blue-line that caromed off Arnott's stick, changed directions, and went into the top corner.
Calgary drew back to within one for the second time in the period on Jarome Iginla's second goal of the night with 3:43 left in the game. However, Vokoun held the fort the rest of the way including a hectic sequence in the final seconds.
Vokoun finished with 25 saves to improve to 10-3-3 lifetime against the Flames.
Nashville has won the past five meetings between the two teams and has lost just once to the Flames in their last 11 games.
JP Dumont also scored for Nashville (6-3-1).
The Predators kicked off a five-game road trip with a fourth straight win away from home. After opening the season with three losses, the Predators have picked up points in their last seven games (6-0-1) and are tied with the Detroit Red Wings for first place in the Central Division.
After playing just once in the past eight days, Calgary (3-5-1) began a busy stretch of five games in eight days. The Flames sit last in the Northwest Division. Matthew Lombardi had an assist to extend his points streak to six games (3 goals, 5 assists).
Leading 1-0 halfway through the second period, Arnott's power-play goal was a back breaker for the Flames. Having killed off two Nashville power-plays earlier in the period, the Flames were unable to kill off Andrei Zyuzin's interference penalty.
Early in the third period, with the Flames on the power-play, Steve Sullivan stole the puck at the Nashville blue-line and raced away on a clean breakaway only to be thwarted by Kiprusoff.
The Flames headed back up the ice where Kristian Huselius threaded a pass to Iginla at the side of the net and the Flames captain tucked the puck inside the goal post.
In the continuation of what's been an early season problem for the Flames, they fell behind on a goal in the final minute of a period.
There was just 13 seconds left in the first period when a stretch of steady pressure in the Flames zone by Nashville eventually resulted in Dumont getting a loose puck and snapping a shot past a besieged Kiprusoff.
Notes:Calgary defenceman Dion Phaneuf was out with the flu marking his first missed NHL game. In his rookie season last year, Phaneuf was one of only four Flames to play in all 82 games. That opened up a spot for rookie D Mark Giordano, who scored twice in his last game back on Oct. 14 ... Sullivan returned to the line-up after missing three games with back spasms ... Kiprusoff is the only goaltender that has played every minute of his team's games ... Calgary LW Jeff Friesen has not scored in his last 25 games.