Guentzel started the rush to Kucherov, who passed it back and forth with Point, and scored from the left post.
"I knew we had a bit of speed," Point said. "'Kuch' made a great play to go under the stick and then he beats his guy to the post there. It was a great pass by him to get it to me with speed and then he does a great job jumping by his guy. He's really good at that."
Gourde increased the lead to 2-0 at 13:45, collecting the rebound of Gage Concalves' shot on his backhand and putting the puck in while falling down.
"A little bit of a dirty goal the second one with the shot, rebound, around the net type goal," Cooper said. "Those are playoff-type goals."
Point scored his 40th on the power play at 14:54 to give Tampa Bay a 3-0 lead. Kucherov collected his 80th assist by moving the puck to Guentzel below the right face-off circle. Guentzel slid it across to Point, who jammed it in from the left post.
"We put the pressure on them, we were getting pucks to the net, couldn't find a goal and then it just seemed like back to back to back," Brodzinski said. "Not tying up guys in front or just small stuff around the net that cost us."
Zibanejad's power-play goal at 3:16 of the second period cut the lead to 3-1, but Vasilevskiy stopped 17 of 18 shots in the second period.
"We needed that second one I thought in the second period to get it to 3-2 and make that push toward the third period," Rangers coach Peter Laviolette said. "That never came."
Kucherov and Guentzel again set up Point for a power-play goal from near the left post at 15:40 of the third period to make it 4-1.