Kuemper was busiest in the second period, turning aside all 14 Lightning shots while protecting a 1-0 lead.
Dany Heatley doubled the Wild's advantage with the eventual game-winning goal 34 seconds into the third.
Tampa Bay's Valtteri Filppula, however, scored with 6:07 remaining and the Lightning put on the pressure on the final minute, seeking a score-tying goal.
Tyler Johnson had Kuemper down but rang a shot off the post with 30 seconds left and the Wild escaped to end a two-game losing streak.
Nino Niederreiter also scored and Jared Spurgeon notched two assists.
Ben Bishop stopped 24 shots for the Bolts, who completed a 1-3-0 road trip.
Notable deaths of 2014 [PHOTOS]