Linemate Daniel Sedin, Henrik's identical twin, had a goal and an assist, with his 25th goal 8:35 into the second putting the Canucks up 4-0.
Henrik Sedin got his third assist of the game on the play after contributing his 12th goal and two assists in the first. Burrows, who had a goal and an assist in the first, also assisted on the Vancouver's fourth goal as the Canucks' top line combined for nine points.
"He's able to make plays," Henrik Sedin said of Burrows, who has 14 goals and 17 assists. "I think a lot of people think that we need someone who just stands in front of the net but we've always said that that's not the case. He joins the rush, he enjoys our style of hockey game and he can make good passes, so it's a lot of fun."
"We knew coming in here our start was going to be important," Luongo said. "We know these guys like to come out strong at home so we talked about that before the game and I think we did a pretty good job. We got a good lead and then we played a good system game the rest of the way."
"We did a good job once we got down but we just can't afford to start the game like that," Senators center Jason Spezza said. "Obviously it was a good sign to see the guys battling and try to chip away at it."
The Senators were without Daniel Alfredsson, who learned earlier in the day that he would be sidelined for at least a week because of a broken jaw.
The Ottawa captain suffered a fracture that won't require surgery when he was hit by a puck shot by Heatley on Tuesday night in a 3-2 overtime loss in Colorado.
The Senators ended a season-high five-game winning streak Tuesday to finish a 4-0-1 road trip and are 5-2-2 overall under Clouston.
Rookie Brian Elliott made 19 saves in his first start for Ottawa since Saturday in Minnesota, when he was pulled after allowing the first three goals in a game the Senators came back to win 5-3.
Burrows opened the scoring with his 14th goal 3:14 in and Henrik Sedin made it 2-0 with his 12th goal at 10:49.
Bieksa scored on a slap shot from the point for a power-play goal at 15:23 that increased the lead to three.
After Daniel Sedin's goal 8:35 into the second made it 4-0, Heatley got his 27th on a power play at 12:37 to put Ottawa on the board.
Fisher drew Ottawa to 4-2 at 16:18 when Senators defenseman Chris Phillips' point shot went in off him while Luongo was knocked into the net after he was bowled over by Canucks defenseman Mattias Ohlund.
Luongo stuck out his left pad to deny Heatley on a breakaway 6:30 into the third.
Demitra scored into an empty net with 11.8 seconds remaining.
On Saturday night, Vancouver's Mats Sundin will play his first game in Toronto since leaving the Maple Leafs as a free agent. "I can't worry about what's going to go on around the rink or before or after the game," said Sundin, the Maple Leafs' all-time leader in goals and points. "I'll go out and once the puck drops it's a hockey game like any other. We're in a race to earn a playoff spot and get into a good position for the playoffs, so that's all I'm going to worry about." ... Daniel Sedin leads the Canucks with 58 points, followed by Henrik Sedin, with 55. ... C Chris Kelly took Alfredsson's place at right wing alongside Heatley and Spezza on Ottawa's top line.