Agnew replaced Gerard Gallant, who was fired Monday, one day after a shutout loss dropped the league's lowest scoring team into last place in the Central Division. Agnew joined the Blue Jackets as an assistant in the offseason after coaching their top affiliate for six seasons.
J.P. Dumont, Vernon Fiddler and Scott Nichol also scored for Nashville, which has won seven of eight overall and eight of its last nine road games. Paul Kariya added two assists.
Rick Nash scored twice and Fredrik Modin tallied a goal and an assist for Columbus, which has lost four of five. Jason Chimera also scored for the Blue Jackets.
Down 3-2 early in the third period, Nash and Modin scored twice in a 1:50 span to make it 4-3 at 9:12. But Legwand and Nichol quickly countered with goals 31 seconds apart just past the midway point to make it 5-4 Predators.
Legwand stuffed home his own rebound at 11:32 to tie it at 4.
After Columbus defenceman Aaron Johnson turned the puck over deep in his own end, Nichol put the puck past goaltender Pascal Leclaire at 12:03 for a 5-4 Nashville lead.
Nash made it 3-3 after taking a pass from Klesla down the right wing and snapping a shot from the circle past Tomas Vokoun at 7:22.
On a similar play, Nash came out of the corner and centred a pass to Modin for a one-timer to give Columbus a 4-3 lead.
Columbus pressured right out of the gate, but Nashville scored first. Positioned in the slot, Dumont redirected Kimmo Timonen's point shot for a power-play goal at 5:21 of the opening period.
Manny Malhotra slid a centring pass to Chimera, who snapped a high shot from the right circle past Vokoun at 16:06. The tally was Chimera's first of the season in 16 games played.
Notes: The game was the first of three in six days between the divisional rivals. ... Since the start of the 2000-2001 season, the Blue Jackets have had four coaches. Only five teams (Florida, Anaheim, Boston, Montreal and New Jersey) have had more during that span. ... Nashville is 8-2 in one-goal games. ... Columbus entered having allowed four short-handed goals, second most in the league.