The Stars were trying to move into a first-place tie with the Red Wings in the Western Conference and scored three unanswered goals in the second period to take a 3-1 lead.
Detroit then overwhelmed Kari Lehtonen the rest of the way, getting the game tied by the end of the second period and running away with a four-goal third stanza.
Eaves forged a 3-3 tie with a power-play goal with 2:14 remaining in the second. He gave the Red Wings a 6-3 lead with 5:53 to go in the third period and added an empty-net tally with 2:14 to play.
Jimmy Howard made 28 saves in Detroit's third straight victory. The Red Wings had lost in each of their previous six trips to Dallas.
Lehtonen allowed six goals on 25 shots.