Stamkos deflected a Nikita Kucherov shot for a goal at 13:41 of the second period to give the Tampa Bay a 1-0 lead.
"It wasn't really pretty tic-tac-toe play," Lightning defenseman Ryan McDonagh said of their offensive play. "It was straightforward and putting the puck to the net.
"You see our goals that we did score coming off of shots that we put with bodies and traffic. That's how you have to score."
Gurianov scored on the rush at 17:49 to tie the game 1-1. It was his 12th goal of the season and third in the past six games.
"We didn't give up a whole lot," Bowness said. "I thought we rebounded very well and dominated the second period, and it was an even third. Most of that offense came from good defense. We didn't give up much, but we created a lot."
Benn scored on his backhand on a breakaway at 9:06 of the third to give the Stars a 2-1 lead.
"That's just how it goes," Benn said. "As long as we stick with it, stick with our game plan and our details, that gives us the best chance to win, and that is what we did tonight."
Stamkos scored his second goal of the night at 18:34 with Vasilevskiy pulled for the extra attacker to tie the game 2-2.
"Give the guys a lot of credit for coming up in the last five minutes, especially during that 6-on-5 with the tying goal," Lightning coach Jon Cooper said. "It was just turnovers and it was fitting that the game ended on a turnover. We got a point out of it, so we'll take that to start here."
Stars forward Roope Hintz left the game after sustaining an upper-body injury during his first shift.
Stars forward Andrew Cogliano left the game at 13:41 of the second period with a lower-body injury.
Bowness said each forward is day to day.
The Stars and Lightning each went 0-for-4 on the power play.
"It wasn't nearly good enough," Bowness said. "I thought we got outworked on the power play. We didn't make good decisions on the rush. It's got to be a whole lot better."
Lightning forward Brayden Point said, "The power play wasn't great tonight, and we didn't generate many high-quality chances. They did a good job and give them credit, but it's on us to work out plays that can generate scoring chances."
