Jimmy Snuggerud found the loose puck off the wall and backhanded it to Buchnevich low at the right dot for the wrist shot to make it 2-1 at 16:21.
Buchnevich also tallied an assist, Robert Thomas had a goal and an assist, and Joel Hofer mad 22 saves for St. Louis (22-29-9), which had lost four of five, including 3-1 to the New Jersey Devils on Saturday.
It was Thomas’ first game since Jan. 10. The forward missed the past 13 games with a lower-body injury and has been away from the team for personal reasons since Wednesday.
Kirill Kaprizov tied Marian Gaborik for most goals in franchise history (219) and extended his point streak to seven games (six goals, four assists) with the lone goal for Minnesota (35-16-10), which has lost two straight but is 6-2-0 in its past eight. Filip Gustavsson made 21 saves.
Kaprizov made it 1-0 on the power play at 16:09 of the second period when Quinn Hughes sent a saucer pass across to Matt Boldy, who picked it up on the backhand and sent it to Kaprizov on the left post for the redirect past Hofer.
With the primary assist on the goal, Boldy extended his point streak to nine games (eight goals, 10 assists).
Logan Mailloux responded to tie it 1-1 at 18:05 with a snap shot from the top of the right circle after getting the pass from Thomas on the rush.
Hofer kept it 2-1 at 19:26 after Wild forward Mats Zuccarello forced a turnover and found Vladmir Tarasenko for a point blank shot.
Thomas scored into the empty net at 19:35 for the 3-1 final.
Wild forward Marcus Foligno did not play with a lower-body injury.
