Connolly assisted on Paquette's goal in the third period and then scored one himself 4 1/2 minutes later.
Lightning goalie Ben Bishop made 21 saves. Lindback stopped 28 shots but gave up five goals.
Jamie Benn scored for the Stars on a rebound at 14:50 of the second.
Dallas completed its preseason schedule with a 4-2 record. Stars goalie Kari Lehtonen, who left Monday's game with a concussion, is expected to play in the season opener Oct. 9.