Ondrej Palat and Ryan McDonagh scored 10 seconds apart in the second period, and Andrei Vasilevskiy made 28 saves for the Lightning (3-3-1), who had lost three in a row, including 5-1 at the Buffalo Sabres on Monday.
"The way last night went, we thought for most of that game, we played well and kind of shot ourselves in the foot," Tampa Bay coach Jon Cooper said. "There's a lot of talk about back-to-backs and how hard they are. Sometimes back-to-backs are needed. We needed a game right after last night. Good feeling the guys would respond. They certainly did tonight."
Tristan Jarry made 26 saves for the Penguins (3-1-2), who have played their six games without centers Sidney Crosby (wrist) and Evgeni Malkin (knee). Pittsburgh had its season-opening five-game point streak end.
"We're putting ourselves in a position to win games," Pittsburgh coach Mike Sullivan said. "I think we're a team that's playing well collectively as a group. The structure is evident. That's important at this particular time. ... We're not perfect. We make mistakes, but they're mistakes of enthusiasm."
Brayden Point gave the Lightning a 1-0 lead 31 seconds into the second. After taking a pass from Alex Killorn in the neutral zone, Point drove past Penguins defenseman John Marino for a backhand to the blocker side.
"I thought we played well," Marino said. "We skated hard. Controlled the majority of the second period, but the chances we gave up were too much."