John Tavares cut it to 2-1 at 3:54 of the second period after Tyler Ennis forced a turnover along the right wall and poked the puck over to him.
"We have to find ways to get better," Tavares said. "We have a quality team, we have a lot of talent, we have a lot of youth, a lot of growth still ahead of us. ... (You) really realize you have to make the most of every chance you get. It's just difficult right now."
Kuraly scored on a wrist shot from the top of the left face-off circle at 2:40 of the third period for a 3-1 lead.
Charlie Coyle (17:26) and Bergeron (19:59) each scored into an empty net for the 5-1 final.
"Well, I personally felt good from the start of the series," Rask said. "I felt good pretty much all year. You know, obviously the workload hasn't been too much, so I feel fresh. It's all about feeling confident and preparing yourself the right way, trusting your teammates. I thought we battled hard for each other all year, and you know, I think it showed again today."