Mantha deflected Alex Biega's shot from the right point to make it 2-1 at 10:10.
"[The Red Wings] got their bounces from working hard," Brind'Amour said. "Some weird goals, but beating us to the net, fighting in front of the net. They earned their two points tonight."
Jordan Staal tied it 2-2 at 14:44 of the first when he skated past his brother, Red Wings defenseman Marc Staal, to a loose puck along the right boards and beat Greiss with a wrist shot off the left post.
Hamilton gave the Hurricanes a 3-2 lead at 9:52 of the second period when drove the net from the left circle and scored on a rush.
"We were chasing the game a little bit, but I still thought we still had some chances," Hamilton said. "It felt like we should have won."
Filppula tied it 3-3 at 16:03. Mrazek tried to clear the puck with his stick during a scramble in front of the net, but it deflected off Staal's right skate and redirected in five-hole.
NOTES: The teams will complete the two-game set here Monday. … Erne has scored nine goals this season after scoring nine the previous two seasons combined. … Trocheck has scored a point in 13 straight games he's played (seven goals, 11 assists); he missed eight in between with an upper-body injury. … Hamilton has scored a point in 18 of his past 21 games (five goals, 17 assists). … Jordan Staal played his 999th NHL game.