Tim Jackman and Curtis Glencross scored 2:06 apart early in the second to put the Flames ahead. But Samuelsson tied it with a perfect shot through Ryan Kesler's screen at 10:40, and put Vancouver ahead with a power-play one-timer from the point through Daniel Sedin's screen less than three minutes later.
Samuelsson now has seven goals and 14 points in his last eight games.
Mason Raymond added two assists as the Canucks bounced back from a 4-3 loss to Anaheim on Wednesday - just their third in regulation in more than two months.
Roberto Luongo finished with 24 saves to remain unbeaten in regulation since Dec. 5 (16-0-5) as Vancouver moved four points ahead of Philadelphia atop the NHL, and nine up on Detroit in the West.
Miikka Kiprusoff made 29 saves for the Flames, who were coming off an overtime loss to Anaheim on Friday night.
Calgary lost in regulation for the first time in 11 games (8-1-2). It jumped from 14th to eighth in the Western Conference with the run, but the losses dropped it back to ninth, a point behind Minnesota for the final playoff spot.
Calgary had three chances to tie it on the power play in the third period, but couldn't convert against an injury-riddled defense.
Rene Bourque did hit the post on a backhand from the slot late in the second chance. But that was the closest the Flames came to beating Luongo, who forced Brendan Morrison wide on a partial breakaway, robbed Olli Jokinen twice with his blocker and stuffed Matt Stajan on a 2-on-1 in the final 10 minutes.
Vancouver was missing three top defensemen after losing Keith Ballard (knee sprain) on Monday, Dan Hamhuis (concussion) on Wednesday and Alex Edler (back surgery) the week before. But veteran Sami Salo was called up from a three-game AHL conditioning stint and returned from tearing his Achilles' tendon in July.
Burrows opened the scoring midway through the first period, fighting off Tom Kostopoulos to bang in a slick cross-crease feed from Mason Raymond. It was Burrows' first power-play goal of the season, and extended his point streak to nine games (seven goals, three assists) - the longest active run in the NHL.
Jackman tied it with his 10th goal of the season on a nice cross-ice pass from Stajan 2:11 into the second period, and Glencross scored for a fourth straight game a couple of shifts later. Captain Jarome Iginla won a battle behind the Vancouver net to Morrison, who quickly fed it out front to Glencross unchecked in the low slot for a one-timer past Luongo's blocker.
NOTES: Calgary LW Alex Tanguay missed a third straight game with a neck strain. ... Canucks C Manny Malhotra assisted on both Burrows goals, his first points in 20 games. ... Veteran Calgary D Steve Staios played a second straight game ahead of Brendan Mikkelson after missing almost two months with injury and sitting out three games as a healthy scratch. ... The game started with a video tribute to the 2010 Olympics, which opened exactly one year ago in Vancouver, introductions of 10 players from both teams that represented their countries, and a ceremonial faceoff featuring seven other Olympians and Winter Games CEO John Furlong.