It is the third win in preseason for the Predators.
Andy Murray and Antoine Vermette scored for Columbus.
Rinne moved out of the crease to make a block and Vermette got his stick on the rebound and fired a shot into an empty net at 12:16.
Dan Ellis replaced Rinne at that point and played the rest of the game.
Jones scored with 1:52 left in the second period. He beat Columbus goaltender Mathieu Garon with a wrist shot high to the left side of the goal.
Daniel Lacosta was in net for Columbus in the third period. Arnott scored the tying goal with 3:59 left. J.P. Dumont centered the pass in front of the crease and Arnott came in from the right side to beat Lacosta with a shot into the left side of the net.
With 21 seconds left in the first period, Tommy Sestito fought Nashville's Jordin Tootoo. He was thrown to the ice by Tootoo and had to be helped off the ice by two of his teammates. He was coherent, but was transported to a local hospital for further evaluation. ... Nashville's Steve Sullivan left the game in the first period with a lower-body injury and did not return. It was said to be a precautionary measure.