Edler challenged Pekka Rinne from the left side, skating deep into the zone and flipping a shot past his right pad. At the other end, Colin Wilson was able to slide a shot under Roberto Luongo from the right, but the puck drifted wide on the far side of the net.
"It's a tight league. Not a lot of separation, and we're going to be involved in a lot of tight games," Luongo said.
The Canucks beat the Predators for the second time in three games this season, though Tuesday's game was the first time the teams met in Nashville since last year's Western Conference semifinals, which Vancouver won in six games.
Ryan Kesler, Byron Bitz and Daniel Sedin scored goals to give Vancouver a 3-1 lead at the first intermission. Luongo had 34 saves in regulation, including one at the horn on Colin Wilson's shot from the point.
Luongo added three saves in overtime and the Canucks remained unbeaten in regulation over their last six games (5-0-1). The Northwest Division leaders have only two regulation losses in their last 14 games (9-2-3).
Sergei Kostitsyn and Mike Fisher scored in the first 5:16 of the second period to tie the game for Nashville, which fell to 14-3-1 over its last 18. Wilson had a goal and Rinne finished with 28 saves.
"That's a fast team over there and we tried to match it," said Nashville defenseman Roman Josi. "I thought we played pretty well and a got a point out of it, just couldn't get that extra point."
On a power play, Kesler beat Rinne with a snap shot from the right side at 11:42 of the first period but Wilson squeezed a shot through Luongo from the left side to tie the game at 1-1 two minutes later.
Bitz's goal came from the slot on a 3-on-2 with 1:39 remaining in the period and Sedin scored just 23 seconds later, stuffing the puck in off Bitz's pass from behind the net.
Kostitsyn got a piece of Kevin Klein's shot from high on the right side for his goal at 4:14 of the second period and Fisher also scored on a deflection 62 seconds later to tie the game at 3-3.
The Canucks are 2-0 on a four-game road trip that continues on Thursday at Minnesota...The Predators had a six-game home winning streak snapped. They play four of their next five on the road.