Goals by Brad Richards, Mark Fistric and Jamie Benn in a 1:14 span in the second period gave the Stars a 3-1 lead. But Eaves struck on the power play after Nicklas Lidstrom scored at even strength to help the Red Wings tie it at 3 entering the final period. Stuart's blast from the point got past goalie Kari Lehtonen, who was screened by Detroit's Justin Abdelkader.
Kris Draper's goal from the left circle at 13:23 of the third, and Eaves' second of the night 44 seconds later gave Detroit a three-goal edge. Eaves completed his hat trick with an empty-netter at 17:46.
The Red Wings were 2-8-0 in their last 10 meetings with the Stars, winning in Dallas for the first time since Jan. 5, 2008.
Hudler got Detroit on the board at 1:36 of the first period, 12 seconds into the game's first power play. Teammate Todd Bertuzzi had possession with his back to the net, and he passed to Hudler low in the right circle. Hudler lifted a shot into an open net before Lehtonen could slide over to cover.
Richards countered on a breakaway at 5:39 of the second period to tie it.
Fistric notched his second goal of the season, and second in two games, on a shot from center point that glanced off Bertuzzi's stick and got past Howard at 6:24 of the second.
Benn needed only 29 more seconds to give his team a two-goal pad when he set up in front of the net and converted Mike Ribeiro's centering pass.
But the Red Wings picked up their intensity with a 15-shot second period.
Lidstrom connected from the slot at 8:56 of the second, and Eaves drew his team even at 3 with a man-advantage goal at 17:38 of the second.
NOTES: Stars D Nicklas Grossman and C Tom Wandell were back in the lineup after missing two games with the flu. ... The Red Wings will be without C Mike Modano, the Stars' career scoring leader, until March due to a lacerated wrist. ... Earlier Wednesday, the Stars announced they had signed D Trevor Daley to a six-year contract extension worth $19.8 million.