The Stars played their fourth straight overtime game and they have won the last three of those -- all on the road against Ottawa, Boston and Detroit.
Dallas rallied from an early 2-0 deficit to tie the game on a goal by Jamie Benn 4:08 into the third. Detroit regained the lead when Pavel Datsyuk scored with 8:26 left, but Cody Eakin again tied it for the Stars on the power play with 1:10 to go in regulation.
Peverley won it by putting a wrister from the top of the left circle past a screened Jimmy Howard.
Kari Lehtonen made 26 saves in the victory. Howard stopped 24 shots in what was Detroit's second straight loss.