Lilja, a defensive-minded defenseman, beat Ward with a slap shot from the left point with 7:20 left in the second period to break a 2-2 tie. It was only Lilja's second goal of the season and fourth in two-plus seasons with Detroit.
"It's always nice to score. It doesn't happen often," said Lilja, who was also named the game's first star. "When it happens that makes it better."
Datsyuk and Holmstrom, who both play on the Red Wings' dominant first line along with Henrik Zetterberg, added goals in the final three minutes of the game. It was Datsyuk's 12th goal and Holmstrom's 14th.
But the goals that allowed Detroit to win the game all came from other sources.
"Earlier it was said that we had no secondary scoring," said Red Wings' coach Mike Babcock. "But they're rounding into shape."
Zetterberg (41 points), Datsyuk (35), and Holmstrom (28) are the team's three leading scorers and are followed by Detroit's top defense pair of Nicklas Lidstrom (26), who had two assists, and Brian Rafalski (24). But Hudler has 20 points and Dan Cleary 17.
"It's 82 games, you've got to help the first line," said Hudler. "They score a lot of goals, but we're going to need everybody."
Cole's second goal of the game, on a power play, tied the game at 2 with 9:24 left in the middle period. He scored on a one-time slap shot from the top of the right circle for his seventh goal.
"It's tough," said Cole. "You have to keep trying to battle back, coming from behind."
Franzen's power-play goal 6:02 into the second gave Detroit a 2-1 lead. He tipped in Cleary's shot for his third goal and second in two games.
Cole's first goal, just 46 seconds into the second period, put Carolina on the board and tied the game at 1. He beat Hasek from the bottom of the right circle.
Filppula gave Detroit a 1-0 lead just 4:35 into the game when jammed in his own rebound for his fifth goal.
"It seemed like we were chasing quite a bit, were in defensive posture quite a bit," Hurricanes coach Peter Laviolette said. "As opposed to having the puck and trying to establish our game."