Henrik Zetterberg scored with 16.4 seconds left in the third to tie it, Justin Abdelkader scored and Jimmy Howard stopped 23 shots to help the Red Wings win their first road game since moving to the Eastern Conference.
Zetterberg sent it into overtime when he pushed a loose puck past Ward after a scramble in front of the net. Ward lost his stick while stopping a shot from Daniel Alfredsson a moment earlier.
Weiss then ended it when he stuffed a loose puck past Ward.
Zetterberg also had an assist for the unbeaten Red Wings, who were blanked until Abdelkader beat Ward 42 seconds into the third.
Detroit shifted from the Western Conference to the East as part of the NHL's realignment. It also moved the Hurricanes into the new Metropolitan Division and the Southeast Division was dissolved.
Dvorak and Gerbe were two of five players skating for the first time in Carolina red.
Dvorak, a veteran forward who came to Carolina's preseason camp on a tryout basis, earned a one-year contract Wednesday while Gerbe signed a one-year free-agent deal in late July after playing parts of the past five seasons with Buffalo.
Dvorak put the Hurricanes up 1-0 with 6:30 left in the first, chipping Jeff Skinner's long cross-ice pass over Howard's shoulder.
Gerbe then struck with 1:49 left in the second, in the final seconds of a holding penalty on Brendan Smith. Gerbe positioned himself near the net, scooped up a deflected shot and whipped it past Howard to put Carolina up 2-0.
NOTES: Carolina RW Alexander Semin and Henrik Zetterberg each rang the post. ... Faulk wore an "A'' on his sweater because regular alternate captain, D Tim Gleason, was out with a concussion. ... This was the first meeting between the teams since March 24, 2012. They play twice more this season.
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