Booth scored for the second consecutive game after going scoreless in his previous 32.
On his first goal, Booth took the puck the length of the ice after a faceoff and fired it past Darcy Kuemper.
Booth's second goal broke a 1-1 tie in the second period and came after Jared Spurgeon whiffed on a pass in the Wild zone, leading to a bad turnover and a point-blank look for Booth.
''We didn't generate a ton of shots, but we were able to capitalize on the ones we did,'' Booth said.
Minnesota, currently holding the first wild-card spot in the West, controlled play for most of the first two periods, but failed to capitalize on four power plays and fell behind 3-1.
Even though his team was generating chances early, Wild coach Mike Yeo was nervous.
''Especially in that first period, we're out chancing them, we're outshooting them, but still. Just didn't quite have the right feel,'' he said.
Ilya Bryzgalov took over for the slumping Kuemper after two periods. Kuemper allowed three goals in 12 shots, the fifth time in his last seven start he's allowed at least three goals.
''Don't feel good about that one,'' Kuemper said. ''Obviously we were controlling the play and to find ourselves down 3-1, yeah I've got to help the guys out a little bit better.''
The switch didn't get Minnesota going. Vancouver killed an early third period power play, and then put the game away on Sedin's goal at 11:12 to make it 4-1.
''I didn't think we played great, but we stuck with it and at the end we came out with a big win,'' Sedin said. ''For sure, it's something to build.''
The goal was Sedin's first in his last 23 games and his first point in his last 13.
Coyle's goal was his third in three games. The center had scored only once in his previous 24 games.
Lack got a little help in the second period from Alexander Edler. Zach Parise stuffed the puck between Lack's pads, but just before it crossed the goal line, Edler swept it away.
''We know it's do-or-die now and we got to come up with the same kind of effort tomorrow,'' Lack said.
Vancouver has won six of its last nine after losing 11 of 12.
Both Phoenix and Dallas were idle on Wednesday. The Canucks now have 78 points, Dallas 79 and Phoenix 82.
Henrik Sedin missed the game with a leg injury and didn't make the trip.
As Minnesota tries to hang on to its playoff position, Yeo has to answer questions about his goaltending situation.
''I want to be careful on that one. I'm not saying that we can't be any better between the pipes, but at the same time there's some quality chances that we're giving up,'' he said. ''Obviously, we have to do our part to make sure those guys are in the right frame of mind.''
NOTES: Wild G Niklas Backstrom and F Jason Zucker each underwent successful surgeries yesterday and should be ready for the start of the 2014-15 season. Backstrom had core muscle surgery and Zucker had a tendon in his left quadriceps repaired. ... F Alexandre Burrows played for Vancouver after missing Sunday's game with a hand injury. ... The Sedins have only played in two games together in March. ... The Wild beings a four-game road trip in St. Louis on Thursday.