Stamkos, who had surgery in March for a core muscle injury, was limited to less than three first-period minutes on the night but made his presence felt with a goal that put his team ahead 2-0 seven minutes into the game.
On his third shift, Stamkos took a pass in the neutral zone, eluded a Dallas defender and then stormed toward the net where he sniped it home from a sharp angle 85 seconds after Nikita Kucherov opened the scoring.
Stamkos did not play during the final six minutes of the first period and was not on the bench when the second period began.
He returned to the Lightning bench about eight minutes into the second frame and took a few quick skates during stoppages but did not play again.
Victor Hedman, Brayden Point and Ondrej Palat also scored for Tampa Bay while Jason Dickinson and Miro Heiskanen scored for Dallas.
Stars goaltender Anton Khudobin allowed five goals on 29 shots and was replaced by Jake Oettinger to start the third.
Game Four is scheduled for Friday.
The entire Stanley Cup Final is being held in Edmonton, one of two Canadian hub cities for the playoffs, to help limit travel and minimize COVID-19 risks. (Reporting by Frank Pingue in Toronto; Editing by Peter Rutherford )