The Hurricanes hadn't won a regular-season game at Detroit since Nov. 14, 1989, when they were still the Hartford Whalers. They did win Game 1 of the 2002 Stanley Cup finals at Detroit, but that was their only victory of that series.
Riley Sheahan scored for the Red Wings in the third period.
Detroit has already clinched its 23rd straight postseason berth, and the Hurricanes are out of the running. The Red Wings outshot Carolina 29-19 but ended up with what could be a costly loss in the race for playoff seeding.
Detroit will be a wild card in the Eastern Conference, so the Red Wings will face either Boston or Pittsburgh in the first round. With 91 points, Detroit is tied with Columbus, and each team has one game remaining.
Philadelphia also has 91 points with two games to play.
Lindholm opened the scoring on the power play, and Tlusty made it 2-0 when he banged a rebound past goalie Jimmy Howard.
Early in the second, Detroit's Tomas Jurco skated in on a semi-breakaway but couldn't put the puck past Ward. At the other end, Eric Staal flipped the puck over a sprawling Howard, only to have Red Wings defenseman Jakub Kindl bat it out of the air with his stick.
Detroit's Justin Abdelkader had much of the net to shoot at when a rebound came his way later in the second, but his attempt went wide.
Sheahan finally jammed the puck past Ward on a power play with 16:17 to play in the game, but Ward made a fine pad save on Abdelkader with about 9:30 remaining, thwarting a 2-on-1 by Detroit and keeping the Hurricanes ahead.
Darren Helm's impressive open-ice move also went for naught when Ward stopped him in close.
The Carolina-Hartford franchise had 16 losses and a tie since its previous victory at Detroit in the regular season.