Vancouver lead the best-of-seven series 3-2 with Game Six scheduled for Monday in Nashville.
"Our backs were against the wall, so we talked about one game and we're going to talk about one game again," Nashville coach Barry Trotz said.
"It was a great character test for everybody. This team is exactly what I told you, they are resilient and a great group to work with day in and day out. We are not perfect, but we do come to play."
Rinne finished with 31 and kept the Predators from being blown away in the first period when Vancouver had the upper hand but had to settle for just a 2-1 advantage.
Legwand opened the scoring with a shorthanded goal early in the first period before Vancouver's Raffi Torres and Ryan Kesler put the home team ahead.
With less than a minute played in the second, Legwand grabbed his second of the game in fortunate circumstances to tie the scores.
From behind the net, the center's pass deflected off a defender's stick and flipped over the net, hit Vancouver defenseman Alexander Edler and went back past a confused looking Canucks goalie Roberto Luongo.
Ward scored twice early in the third period to give the Predators a 4-2 lead before Kesler pulled one back for the Canucks with 3:46 left to play.
Vancouver pressed for the tying goal but were denied by Nashville netminder Rinne.
"For us tonight we put our focus on playing a good game and we came out good, but we had a couple of mistakes that they made us pay for," said Canucks coach Alain Vigneault.
"It was a hard-fought game, it's not easy to finish off a team and we're going to get another opportunity in Game 6."
(Reporting by Mike Mouat in Windsor, Ontario. Edited by Patrick Johnston)
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