Dakota Mermis and Marcus Johansson each notched one goal and one assist, while Mats Zuccarello and Jonas Brodin also scored for the Wild, who have lost two straight games.
Joel Eriksson Ek and Pat Maroon collected two assists apiece and goalie Filip Gustavsson stopped 49 shots.
But Jenner buried a rebound just under three minutes later to card his fourth of the season.
The Blue Jackets were without Patrik Laine, who was injured in the final seconds of Friday's win over the Calgary Flames.
Rasmus Andersson was handed a four-game suspension for the hit, which has Laine sidelined on a day-to-day basis.
Persons:
Adam Fantilli, Jack Roslovic, Minn, Justin Danforth, Kent Johnson, Boone Jenner, Elvis Merzlikins, Dakota Mermis, Marcus Johansson, Mats Zuccarello, Jonas Brodin, Joel Eriksson Ek, Pat Maroon, Filip Gustavsson, Roslovic, Columbus, Danforth, Johnson, Mermis, Zuccarello, Ryan Hartman, Ivan Provorov, Brodin, Jenner, Johansson, Patrik Laine, Rasmus Andersson, Laine
Organizations:
NHL, Columbus Blue Jackets, Minnesota Wild, Blue Jackets, Dakota, Columbus, Fantilli, Calgary Flames, Thomson
Locations:
Saint Paul, Minnesota