Stastny tied the game 3-3 at 15:56 of the third period, 2:54 after Bellemare appeared to tie it when he scored on a rebound from a Stastny wraparound attempt, but a video review determined Bellemare kicked the puck in.
DeBrincat gave the Blackhawks a 1-0 lead at 4:36 of the first period off a backhand mid-air swat.
Kane appeared to make it 2-0 at 11:44 when he backhanded a rebound off Fleury's pad, but it was determined Brandon Saad was offside following a Vegas challenge.
Kane made it 2-0 at 15:20 with a power-play goal from the right face-off circle with Dylan Strome screening in front.
"I think the guys did a really good job of moving the puck around quick tonight," Kane said. "Break-ins are solid and you end up going 2-for-4 [on the power play]. It's been a confident part of our game lately."
Tuch cut it to 2-1 at 1:34 of the second period, poking in a rebound after Delia was unable to cover it. Tuch has 11 points (three goals, eight assists) in the streak.
"It's good to see myself have a little consistency, more than last year, that's for sure," Tuch said. "I would have a point or two points in a game and then not have a point for three, four games last year, and that's not what I wanted to do."
DeBrincat extended the lead to 3-1 on the power play at 7:22 on a one-timer off a pass from Kane.
Carpenter made it 3-2 at 19:06, skating into the offensive zone and scoring glove side from the left face-off circle.