"Good for our franchise," Trotz said. "Sort of like we've arrived."
Nashville is a point ahead of Detroit with four games left in the regular season to be the fourth-seeded team with home ice in the first round of the Western Conference playoffs.
"It doesn't mean anything right now," Nashville's Shea Weber said. "It gives us some confidence that we can come in here and win. If we don't win against Chicago (Saturday), we'll be back in the same situation with Detroit right on us."
Trotz is the fifth coach to win 500 games with one franchise, joining the New York Islanders' Al Arbour, Buffalo's Lindy Ruff, Chicago's Billy Reay and Montreal's Toe Blake.
David Legwand, who like Trotz has spent his entire NHL career in Nashville, said it was a "great" accomplishment.
"All of us are proud of him for what he did," Legwand said.
Predators general manager David Poile, whose savvy drafting has helped the smaller-market franchise consistently win, is the first NHL general manager to win 500 games with two teams. He helped the Washington Capitals win 594 games from 1982-97 before getting the Predators ready for the 1998-99 season, their debut in the league.
"I admire him for how he's treated me and how he treats everybody," Trotz said.
The Predators have won three of their last four games.
Nashville split the six-game season series with Detroit in their last scheduled game, but the teams might meet again for the third time in the postseason.
The Red Wings were held scoreless on three power plays in the second period in part because Rinne made a sprawling glove save to prevent Henrik Zetterberg from scoring off a rebound.
"We had some real good looks," Detroit coach Mike Babcock said. "But their goaltender made some real good saves, particularly on (Zetterberg)."
Detroit's Jimmy Howard stopped 23 shots after missing four straight games with a groin injury.
"I felt really good out there," Howard said. "I just need to continue to get out there and play."
Detroit spoiled Rinne's shot at a shutout with with 3:03 left when Jiri Hudler flicked a shot into the open net off Zetterberg's cross-crease pass. Weber added an empty-net goal in the final minute.
The Red Wings are struggling down the stretch toward their 21st straight postseason with eight losses in its last 10 games. The Red Wings have gone from leading the NHL in points to getting mathematically eliminated from catching Central Division-leading St. Louis.
"It felt like we couldn't lose here, but then the injury bug hit and things tailed off for us," Howard said. "But now we've pretty much got all our guys back, so we just got to find a way."
The Predators entered the game having killed 39 of the previous 43 penalties against them and refused to let an extra skater be an advantage for Detroit in the pivotal second period.
"We got to get playing way better than we have and feeling better about ourselves," Babcock said.
Nashville's Roman Josi (upper body) was in the lineup after missing nine games, Martin Erat (upper body) played after missing two games and Jordin Tootoo was back after missing a game following a fight. ... Howard had played in just eight of Detroit's previous 25 games, limited by a broken finger and groin injury shortly after his first All-Star Game. ... Rinne is 11-5-3 against the Red Wings in his career with four shutouts. Zetterberg had four goals and four assists in his previous four games. ... Nashville is 32-3-4 when it scores first and 29-2-3 when leading after two periods. ... The Red Wings are three points away from extending their NHL record with 12 straight 100-point seasons.