Ivan Barbashev had three assists, and Jordan Binnington made 32 saves for the Blues (15-5-6), who were 0-1-1 in their previous two games.
"I thought it was a good hockey game all around," St. Louis coach Craig Berube said. "Back and forth. We played well. It was a good game. I thought our penalty kill was good (3-for-4). I know we gave up the one, but for the most part it kept them off the scoreboard. Big power-play goal for us in the third. Overall, a pretty solid game."
WATCH: [All Blues vs. Lightning highlights]
Nikita Kucherov had a goal and two assists, Brayden Point had a goal and an assist, and Andrei Vasilevskiy made 29 saves for the Lightning (12-8-2), who had won three straight.
"I thought we played hard. I thought we battled and competed," Point said. "Every line seemed to be working hard. It was tough to come up with nothing, but there is a lot to build on."
Kucherov gave Tampa Bay a 1-0 lead at 3:53 of the second period, scoring off a face-off win by Point when his shot redirected five-hole off Blues forward Zach Sanford.
Sundqvist tied it 1-1 at 5:31 with a shorthanded goal on a breakaway, and he made it 2-1 at 8:40 with a slap shot that beat Vasilevskiy five-hole from the top of the right face-off circle.