Boeser put Vancouver ahead 2-1 at 3:57 of the second period on a give-and-go with J.T. Miller.
"I thought we kind of struggled today, but also, I felt like they played really well," Stars defenseman Esa Lindell said. "They were so tight on us, and all over our execution wasn't there. Feels like they were coming at us all the time, and we didn't really have the momentum today."
Rathbone pushed it to 3-1 at 5:30 on a one-timer from the high slot. Elias Pettersson had a secondary assist on the goal to extend his NHL career-high point streak to 11 games (five goals, 10 assists).
"We've been working on [defensive] zone structure a lot lately and just winning some battles in our net front," Demko said. "I think they're the first team in the League in tips with traffic and that stuff. Obviously, they're going to get some looks in that regard.
"After that first shot was on net, I thought our [defense] did a great job of eliminating second chances and boxing those guys. I was really proud of the guys."
NOTES: Miller has 18 points (nine goals, nine assists) in his past 11 games. ... Canucks forward Vasily Podkolzin left the game after blocking a shot with 11:07 remaining in the third period. ... Stars defenseman Miro Heiskanen's 12-game point streak ended (four goals, 16 assists).