The Badgers extended their conference scoreless streak to 44 2/3 innings before touching Minnesota senior pitcher Piper Marten for a pair of two-out runs in the bottom of the fifth inning.
Layne made the runs hold up, hurling her second complete-game shutout of the season. She allowed six hits and three walks and struck out one, improving to 13-12 on the season.
Marten (20-12) allowed just six hits and no walks while striking out nine in a complete game of her own.
Four of the Badgers hits, though, came in the fifth inning. With two outs and runners on the corners, freshman center fielder Sam Polito singled through the left side of the infield to drive in sophomore second baseman Emily Friedman. Freshman third baseman Athena Vasquez followed with a double to left, driving in freshman pinch runner Nicole Simmons to put Wisconsin ahead 2-0.
The Badgers improved to 29-27 overall, 6-13 in the Big Ten. Minnesota fell to 32-22, 9-10.
The win snapped Wisconsin's seven-game conference losing streak. The Badgers, who have now won two straight overall, last won a Big Ten game April 18 against Purdue.