Jones opened the scoring at 3:18 of the first period and completed it with a power-play goal at 1:26 of the third, redirecting a shot by Cal O'Reilly.
Patric Hornqvist and Francois Buillon also scored for the Predators, who were outshot 11-2 in the first period and 38-23 for the game.
Buillon put the Predators up 3-2 at 17:35 of the second period after taking a pass from behind the goal line by Michael Santorelli. Buillon was low in the left faceoff circle when he put a slap shot on net before goalie Steve Mason could cover the near post.
It was similar to Nashville's goal earlier in the period except on the opposite side. The Predators (4-2-0) had their first shot in 19 1/2 minutes just seconds before Hornqvist scored on the power play at 3:17 to break the 1-all tie.
Nash made it 2-all on the power play at 16:47 with a low drive to the stick side of Ellis. Nash was positioned at the top of the left circle when he received a drop pass from Fedor Tyutin.
Columbus (4-3-1) lost for the first time in five games. It opens Saturday against Minnesota.
Nashville plays at Dallas on Saturday.
Blue Jackets defenseman Mike Commodore and forward Kristian Huselius have not played since getting the flu a week ago. ... Nashville captain Jason Arnott and alternate captains Shea Weber and Martin Erat did not play. Neither did forward Jordin Tootoo. Forward Wade Belak sat because of a groin injury. ... Hornqvist led the Predators in preseason points (seven) and tied David Legwand with five assists. ... Derick Brassard and Jakub Voracek led Columbus with seven points. Brassard had a team-high five assists in five games. Voracek and Nash had three goals.