Aaron Gagnon ended Dan Ellis' shutout bid 1:19 into the third period to make it 2-1, but Hall and Mattias Ohlund added goals for Tampa Bay.
Ellis made 17 saves, and Dominic Moore also scored for the Lightning.
Philip Larsen added a third-period goal for the Stars.
Ellis was signed as a free agent in July to compete with Mike Smith to be Tampa Bay's No. 1 goaltender. Smith is out for at least a week because of a broken right ring finger.