EDMONTON, Alberta -- With a pair of first-period assists in Game 2, Tampa Bay Lightning winger Nikita Kucherov matched -- then surpassed -- Tampa Bay's record for most points in a single postseason.

With 28 points (six goals, 22 assists), Kucherov bettered Brad Richards' franchise record, which was set during the team's 2004 Stanley Cup run. Both of Kucherov's assists on Monday were gorgeous passes and helped ignite Tampa Bay's slumping power play. Kucherov also leads all Lightning forwards in ice time, shouldering 21:47 a night while captain Steven Stamkos remains out of the lineup.

But after leading the Lightning to a 3-2 win over the Dallas Stars on Monday, to even the Stanley Cup Final 1-1, Kucherov is still looking for more.

"We didn't come here to break records," the 2019 Hart Trophy winner said. "We came here to win a Cup."

Kucherov, 27, is having a dominant summer -- even as he seems a bit banged up after 21 games of postseason games this summer. Monday's game was a microcosm for just how involved Kucherov has been in every aspect of the Lightning's game.

In the first period alone, Kucherov took a big hit from Jamie Benn, got high-sticked and briefly went to the dressing room after crashing alongside 6-foot-7 defenseman Jamie Oleksiak into the boards. Kucherov then returned -- and set up power play goals for linemates Brayden Point and Ondrej Palat.

That type of period can often keep a coach on edge.

"If he were a little younger, it probably would have concerned me," Tampa Bay coach Jon Cooper said. "But this year, it has not. The attention he gets is unparalleled. You're getting that attention for a reason -- it's because you're pretty darn good. But you can't let anyone see you sweat. They're going to make it tough on you and you need to fight through it. Respect is earned and it's gained when you fight through stuff. And he's found a way to keep his emotions in check and really grind through players being hard on him. That's why he's being rewarded on the points side of things. ... It's really fun to watch."

Already this summer, Kucherov passed Hockey Hall of Famer Martin St. Louis to become the franchise's all-time playoff goals leader (34).

Kucherov's assist to Point on Tampa Bay's first goal -- the first time in six games the Lightning struck first -- came on a tic-tac-toe sequence with Victor Hedman. Three minutes later, also on the power play Kucherov faked a one-timer -- which he sold well, especially considering Kucherov leads the team with 78 shots this summer. Instead, he sent a pinpoint pass across the seam to Palat, who had a wide open net.

Tampa Bay's power play had entered Game 2 on a 0-for-14 cold stretch, which dated back four games.

Kucherov said he left Monday's game briefly only because his visor was broken -- coincidentally after absorbing two big hits.

"Tough start, I guess," Kucherov said. "It's playoffs, you have to play no matter what."

Stamkos is inching closer to a return, and even took part in morning skate on Monday. But his absence hasn't been felt as much, in part due to the leadership of Kucherov.

By winning Game 2, the Lightning have yet to lose consecutive games this summer. They are 6-0 in games following a loss. Kucherov has nine points in those wins.

"Everybody is amazed by the wonderful skill plays he makes," Cooper said. "But you look at his battle level, you look at when he goes in for 50-50s, or 40-60s and still comes out with the puck, it's impressive. That's it for me, how hard he's working. There's gritty things that guys get a lot of accolades for that don't have his skill level. But when you have his skill level and he still does that, it's pretty impressive."