The Canucks' top line produced Daniel Sedin's 10th goal 33 seconds into the game. The trio combined efforts once again, 22 seconds into the third on Burrows' first goal of the season.
Burrows recorded his first points in five games since returning from off-season shoulder surgery. He had 35 goals and 32 assists for 67 points -- all career highs -- while playing with the Swedish twins last season.
"It means a lot," Henrik Sedin said. "It has a trickle-down effect on the whole team. If he can play with us, you've got the second line together and you've got a third line that has been really effective for us, and if you can keep them together, too, it's tough for teams to match up against us."
Ryan Kesler scored his second goal of the game 49 seconds later to put the Canucks up 4-1 at 1:11. Tanner Glass and Mario Bliznak also scored as Vancouver got four goals in the third.
Roberto Luongo made 33 saves for the Canucks, who ended a six-game winning streak Tuesday with a 2-0 loss in Montreal.
"It was a good bounce-back game," said Kesler, whose first goal of the game midway through the second made it 2-1 and put Vancouver ahead to stay. "I thought the first period we were a little sloppy. We were turning over pucks. At the end of the first we kind of re-established ourselves by just chipping it in and making it a simple game."
Vigneault, who has 191 victories with Vancouver, became the 39th NHL coach to reach the 300-win milestone.
"Obviously for 300 I'm happy about that but I'm more happy about the two points we got tonight," said Vigneault, who won 109 games with Montreal from 1997-2000.
Ottawa ended a four-game winning streak.
"It was a good hockey game for 40 minutes," Senators center Jason Spezza said. "We just gave them too many quality chances."
Alexei Kovalev recorded his 998th career point with an assist on Regin's goal.
Pascal Leclaire stopped 27 shots in his first start since injuring his groin in the opening minutes of a 5-1 win over Carolina on Oct. 17.
The Sedin twins finished off a 2-on-1 initiated by Burrows' flip pass up the ice from his own zone to give Vancouver an early 1-0 lead.
Henrik Sedin took the puck off Senators captain Daniel Alfredsson and drove in with his brother, feeding a set-up past Gonchar which Daniel Sedin put into the left side of the net on the first shot faced by Leclaire in four weeks.
Henrik Sedin got his second assist early in the third as Daniel Sedin fed a pass from behind the net to Burrows, who was left alone at the edge of the crease to score his first goal in four games.
Glass scored his first goal at 11:03. Bliznak added his first NHL goal at 16:36 to make it 6-1.
Former NHLers Howard "Rip" Riopelle and Tony Licari, both Ottawa natives and Royal Canadian Air Force World War II veterans, took part in a ceremonial faceoff prior to the game. Riopelle spent three seasons with the Montreal Canadiens in the late 1940s. Licari played nine games with Detroit in 1946-47. ... Canucks RW Rick Rypien fought with Matt Carkner and Chris Neil in the second. ... Senators G Brian Elliott sat after making 11 starts in a row following Leclaire's injury. ... A sold-out crowd of 19,191 was on hand.
Copyright by STATS LLC and The Associated Press
Arena: Canadian Tire Centre Location: Ottawa, Ontario
Referees: Wes McCauley, Chris Ciamaga Linesmen: Michel Cormier, Steve Barton
Attendance: 19,191 (103.7% full)
Team Stat Comparison
Power Play Goals
Power Play Opportunities
Shots on Goal
Daniel Sedin (10)
Assists: Henrik Sedin, Alex Burrows
Peter Regin (1)
Assists: Alex Kovalev, Chris Campoli
Ryan Kesler (6)
Assist: Jannik Hansen
Alex Burrows (1)
Assists: Daniel Sedin, Henrik Sedin
Ryan Kesler (7)
Assists: Mikael Samuelsson, Mason Raymond
Tanner Glass (1)
Assists: Andrew Alberts, Rick Rypien
Mario Bliznak (1)
Assists: Tanner Glass, Christian Ehrhoff