Jamie Benn had a goal and an assist for the Stars, who have lost three of their last four games. Mark Fistric and Brad Richards were the other players to register a goal for Dallas, which has lost three in a row on home ice.
Kari Lehtonen let in six goals on 25 shots in the loss.
Detroit took the lead, 4-3, only 5 1/2 minutes into the final period when a strong Detroit possession was finished by Stuart's slapper from the point off a pass from Hudler.
Detroit gained a two-goal cushion thanks to Darren Helm's fore-checking that worked away a loose puck to Eaves. He then sent it to Draper, who ripped a one-timer past Lehtonen with 6:37 left in regulation.
Only 44 seconds later, Eaves tapped home Johan Franzen's crossing pass for a 6-3 advantage and Eaves added an empty netter to make up the final score with 2:14 left that capped his trifecta.
"We came out in the third and played a little bit sloppy," said Stars forward Brenden Morrow. "We over-pursued and lost coverage. They capitalized on our mistakes."
The Red Wings opened the game's scoring during Steve Ott's tripping penalty in the first minute and a half of play. Hudler recorded the power-play goal with a snap shot from the right circle off a pass from Todd Bertuzzi.
Dallas came out quickly in the second period by scoring three goals in 74 seconds to take a usually-solid 3-1 advantage.
Richards started the rally at the 5:39 mark with a wrist shot. Fistric then gave Dallas the lead, 2-1, with a slapper at 6:24, and Benn finished out the run by tucking the puck off the right leg of Howard at 6:53.
Detroit fought back, though, scoring the final two goals of the second period. Lidstrom received a pass from Valtteri Filppula and slapped it home just shy of nine minutes played. Eaves knotted them game at three apiece heading into the final period with the Wings' second power-play goal of game at the 17:38 mark.
Eaves, a Boston College product, is now one score off his 2009-10 total of 12...The Red Wings' output was their most in any game at Dallas since the Stars relocated from Minnesota in 1993, and the seven goals were the most for the Wings on the road against the Stars franchise since a 7-1 win at Minnesota on March 7, 1993...Detroit improved to 11-5-1 on the road this season...Before the game the Stars inked defenseman Trevor Daley to a six-year contract extension worth $19.8 million...Franzen and Bertuzzi each had two assists...Detroit was outshot 31-26, but was 2-for-2 on the power play, while Dallas was 0-for-4.