Kucherov gave the Lightning a 1-0 lead at 3:26 of the first period, scoring with a one-timer from the high slot off a pass from Steven Stamkos shortly after a power play expired. He has 100 points (28 goals, 72 assists) in 71 games this season.
Killorn extended the lead to 2-0 at 6:30 of the second period. He slowly skated into the zone while looking for a pass, then after Damon Severson went down to the ice he cut to the slot and quickly shot five-hole on Vanecek.
"To put it in a nutshell, I really liked our first period and the first eight minutes of the second period," Lightning coach Jon Cooper said. "We scored that second goal after they had a couple of chances … then an inexcusable goal off a face-off right away. That never should have happened. That just triggered their momentum. Then it was just senseless turnovers and managing the puck."
Bratt scored nine seconds after Killorn to cut it to 2-1. He got control of the puck while skating through the slot before shooting glove side on Vasilevskiy from the edge of the left circle.
"Obviously, that was really important," Bratt said. "I think we felt as a group that we were playing good hockey. We came out strong, and obviously that goal was kind of a break for us. We got a good face-off play that worked and we got a goal out of it, and that started the momentum for us. That was huge."
Bratt then tied it 2-2 at 9:22 with a shot from the point through traffic.
"We started managing the puck horrendously and we invited them into the game," Lightning forward Pierre-Edouard Bellemare said. "We have control of the puck in the first. In the second, we have a few turnovers. It's on us. Despite the first period, they were really patient in the second, waiting for us to make mistakes."