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.
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.