Burrows scored twice in the third period to lead the Canucks to a 3-1 victory over the Nashville Predators on Tuesday night.
Vancouver clinched the top spot in the West and set a franchise record with their ninth straight road win.
Mike Fisher scored for Nashville.
"We talked about getting in, getting first in our division, and if the conference was there, go for it," Vancouver coach Alain Vigneault said. "We did it and we clinched it. It is a good moment for our group."
Vancouver dominated the third period, outshooting the Predators 14-2.
"We just didn't have enough of that bite in our game, that determination, that urgency, you can use a multitude of words," Nashville coach Barry Trotz said. "We managed the game pretty well in the first two periods. The last thing you want against a team like the Vancouver Canucks is to be on your heels right off the start of the third period when you are up by a goal."
"I saw it was a turnover, and I knew that Danny had it," Burrows said. "I knew he was going to thread the needle to me, and it was a perfect pass right on my stick."
Earlier in the third, Burrows drew Vancouver even at 1:17.
Behind the Nashville net on the left side, Daniel Sedin sent a pass to twin brother Henrik on the right side, where he quickly fired a pass to Burrows all alone in front of Rinne. Burrows beat Rinne with a one-timer for his 23rd goal.
"That early goal really helped us," Henrik Sedin said. "When Burrows put that in, you could tell they were back on their heels a little bit and we took over the game. Sometimes all you need is a goal like that."
At 14:01 of the second, Jonathon Blum's shot from above the right circle was stopped by Roberto Luongo, but the rebound ended up at the bottom of the right circle where Fisher was there to corral the puck and fire it high above the fallen goalie.
"We played OK the first couple of periods, and then we came out a little flat in the third," Fisher said. "They were more hungry than us, and we didn't realize the situation and respond."
Fisher broke a 17-game goal-less stretch Saturday, and now has three goals in two games.
Aaron Rome added an empty-net goal in the final minute. It was his second NHL goal and first in 109 games.
Notes: In the four games between the teams this season, there were no goals in the first period. ... Canucks D Dan Hamhuis missed the game because of a concussion sustained in Atlanta on Sunday. Hamhuis played the first 483 games of his NHL career with the Predators. ... Rinne has started 37 of Nashville's last 41 games. ... With an assist, Nashville LW Sergei Kostitsyn extended his point streak to seven games.