Sutter was a hero in his first game back after missing 21 games with a problem in his mid-section. He took Alex Edler's long pass from behind the net just outside the Wild blue line, eluded a defender, and beat Devan Dubnyk with a shot from the slot.
The Canucks overcame a late 2-1 deficit to pull out their second straight win, just their fourth win in the past 17 games.
The Wild saw its modest victory run end at two games.
Loui Eriksson and Thomas Vanek also scored for Vancouver, while Edler had two assists. On the winning goal, Edler calmly waited with the puck behind his net while the Canucks made a line change.
Jason Zucker and Daniel Winnik scored for Minnesota.
Zucker opened the scoring on a power play at 4:59 of the first period as he one-timed Mikael Granlund's pass. The goal was Zucker's second in two games. Before Saturday, he had not scored since Dec. 27.
Eriksson drew the Canucks even about 12 minutes later, culminating a three-way passing play with Edler and Henrik Sedin. The goal was Eriksson's first since he netted a pair on Nov. 30 against Nashville.
With the goal, Eriksson now has points in two straight games after being held without a single point in six straight contests.
The second period was scoreless, although the Wild kept the Canucks hemmed in their own zone in the latter part of the session.
Winnik gave the Wild a 2-1 lead at 12:14 of the third period as he one-timed Eric Staal's pass from the corner. But Vanek managed to tie the score just over two minutes later as Dave Gagner's harmless-looking shot went in off him.
Vancouver winger Daniel Sedin missed the game due to back spasms. Earlier Sunday, the Canucks returned winger Nikolay Goldobin to Utica of the American Hockey League.
One of the biggest cheers came before the game as fans, watching televisions on the concourse, celebrated the Minnesota Vikings' improbable last-second comeback victory over the New Orleans Saints.
--Field Level Media
Vancouver | Minnesota | |
Loui Eriksson 2 | Points | Daniel Winnik 1 |
Loui Eriksson 1 | Goals | Daniel Winnik 1 |
Alexander Edler 2 | Assists | Mikael Granlund 1 |
N/A | Power Play Goals | Jason Zucker 1 |
N/A | Short Handed Goals | N/A |
Jacob Markstrom .913 | Save Percentage | Devan Dubnyk .880 |
Jacob Markstrom 21 | Saves | Devan Dubnyk 22 |
Team | Shots | Goals | Power Play | Penalty Kill | Penalty Mins | Face Offs Won |
Vancouver | 25 | 3 | 0-1 | 0-1 | 2 | 24 |
Minnesota | 23 | 2 | 1-1 | 1-1 | 2 | 29 |