Dallas ends the regular season at the Chicago Blackhawks on Sunday and Monday. Nashville hosts the Carolina Hurricanes on Saturday and Monday. The team that qualifies will play the Hurricanes in the first round.
"We had to win tonight, clearly," Stars coach Rick Bowness. "We did what we had to do tonight, now we're going to need a little help. If we get some help from Carolina, we feel good about our game going into Sunday."
Curtis McElhinney made 26 saves for the Lightning (36-15-3), who lost in regulation for the first time in eight games (6-1-1).
"We didn't play very well," Lightning coach Jon Cooper said. "We didn't execute. We didn't defend well, and we didn't compete hard in the way that we normally do. We turned the game into a little bit of a one-on-one game, not only with but without the puck."
The Lightning loss allowed the Hurricanes to clinch the Central title. Tampa Bay will play the Florida Panthers in the first round of the playoffs.
The Panthers and Lightning are tied for second place in the division. They play their final two games at Florida on Saturday and Monday to determine second and third place and home-ice advantage for their playoff series.
Jamie Oleksiak gave the Stars a 1-0 lead at 5:50 of the first period with a shot from close range.
Pavelski extended the lead to 2-0 at 5:17 of the second period when he took a lead pass from Hintz after coming out of the penalty box and scored on a breakaway.
"Obviously we had to be desperate tonight," Pavelski said. "We did a lot of good things. Early on we got pucks behind them, forechecked, we controlled the play that way. It gave us a boost, I think, for sure."
Blake Coleman made it 2-1 at 11:11 of the second with his sixth goal in his past eight games.
"A lack of attention to detail; obviously we've been pretty strong in the late run that we've been on," Coleman said. "For whatever reason we had some big, glaring errors defensively and left [McElhinney] out to dry, unfortunately. And they were able to convert."