Pettersson made it 3-1 with a one-timer at 6:51 of the second period and scored his second on a breakaway he created with a blocked shot to make it 4-2 at 6:29 of the third.
"Good defense leads to good offense," Pettersson said. "In the defensive zone, if you have to block a shot for us to win, you do it."
[WATCH: All Wild vs. Canucks highlights]
Pettersson leads NHL rookies with seven goals and 10 points in seven games. He is the 21st player in NHL history and the eighth in the League's modern era (since 1943-44) to score at least seven goals in his first seven games.
"It's always fun to score, but I think the biggest thought in the team was to bounce back from our last home game against Pittsburgh," Pettersson said.
Video: MIN@VAN: Pettersson blasts home big one-timer
Jacob Markstrom made 31 of his 37 saves in the second and third periods for the Canucks (7-6-0), who had lost two in a row, including 5-0 to the Pittsburgh Penguins on Saturday.
"[Pettersson] was good tonight, but I don't want it to be just about him, there was a lot of good efforts," coach Travis Green said. "Markstrom] was great, he wasn't just good. They had the heat on us, and I like how hard our guys played, but [Markstrom] was a rock back there."
Rookie forward Jordan Greenway scored his first NHL goal, and Devan Dubnyk made 26 saves for the Wild (6-3-2).
"We just didn't have the bounces tonight," defenseman Matt Dumba said. "They had lots of shots and good movement, but it's tough. You can't do that to a team that is as opportunistic as they are."
Video: MIN@VAN: Pettersson scores second goal on breakaway
The Canucks played without top-pair defensemen Alexander Edler (knee) and Christopher Tanev (hip) because of injury for the third straight game, and they lost shutdown center Brandon Sutter to an upper-body injury at 4:04 of the second period.
"That was a gutty performance by our group, especially after [Sutter] went down," Green said. "We had a lot of guys step up."
Sutter was favoring his right arm after hitting the boards awkwardly.
"It's not day to day, so it will be at least weeks," Green said.
Markus Granlund gave the Canucks a 1-0 lead when he scored from the slot at 7:17 of the first period, converting a pass from new linemate Bo Horvat from below the goal line.
Video: MIN@VAN: Granlund buries Horvat's centering feed
It was the eighth time in nine games the Wild allowed the first goal, but they got it back 35 seconds later.
Greenway, who was recalled from Iowa of the American Hockey League on Sunday after he had a hat trick Saturday in one of two games after being sent down, banged in the rebound of his own shot to tie it 1-1 at 7:52.
"It would have been a lot nicer to get a win with it," Greenway said. "I really wanted to get pucks to the net, go to the net, just like I did a couple of days ago in Iowa. It worked out for me. I might keep doing it."
Minnesota was an NHL-best 5-1-1 when the opponent scores first, but Jake Virtanen put Vancouver ahead 2-1 at 5:15 of the second period when he scored on the power play with a shot from the high slot through a screen on the rush.
"You keep doing that too often, I told them, it's going to happen," Wild coach Bruce Boudreau said. "Nobody is able to come back all the time if you're going to start that slow."
Video: MIN@VAN: Greenway scores first regular season goal
Ryan Suter scored on the power play to get the Wild to within 3-2 at 14:37.
Ben Hutton scored into an empty net with 40 seconds left for the 5-2 final score.
They said it
"From the first few games I've been feeling much better out there. At the same time I think there's a lot of (room) for improvement and we can get more scoring chances, offensively we can create more. -- Wild forward Mikael Granlund, who had an assist to extend his point streak to eight games (five goals, five assists)
Video: MIN@VAN: Suter pots power-play goal through traffic
"Super nice to have [Elias Pettersson] in the lineup, and what he brings is unbelievable and he gets the building going too like no other, like [Henrik Sedin] and [Daniel Sedin] used to do. We can feed off that." -- Canucks goalie Jacob Markstrom on the crowd's reaction to Pettersson's breakaway goal
Need to know
Granlund is tied for the second-longest active point streak in the NHL with Brent Burns and Timo Meier of the San Jose Sharks behind Sebastian Aho of the Carolina Hurricanes (11). Granlund is four games shy of his Wild-record 12-game streak from Jan. 12-Feb. 4, 2017. ... Greenway scored April 15 against the Winnipeg Jets in Game 3 of the Western Conference First Round to become the first player in Wild history to score his first goal in the NHL in the Stanley Cup Playoffs.
Wild: At Edmonton Oilers on Tuesday (9 p.m. ET; SNW [joined in progress], SNOL, FS-N, FS-WI, NHL.TV)
Canucks: Host the Chicago Blackhawks on Wednesday (10 p.m. ET; NHLN, SN, SN360, SN1, WGN, NHL.TV)
Video: Pettersson scores twice as Canucks beat Wild, 5-2