The Stars have lost four in a row, averaging only a goal a game during the slump.
Tampa Bay took a 1-0 lead into the third period thanks to Purcell's goal with 1:12 left in the first.
Tom Wandell tied it 1:22 into the final period, but Purcell put a backhander past Kari Lehtonen 2:14 later. Tampa Bay has won two in a row after losing seven straight.
Mathieu Garon collected the victory with 27 saves. Lehtonen stopped 20 shots.