The Senators are 2-0-1 all-time against the Wild, including a 4-1 triumph here on January 19, 2002.
Ottawa improved to 1-1 on its homestand after a 4-0 blanking of Nashville on Saturday. Magnus Arvedson scored two goals and Daniel Alfredsson and Brian Pothier had one apiece for the Senators, who are 7-2-1 in February.
Patrick Lalime made 18 saves for his league-leading eighth shutout of the season and 28th of his career. Lalime broke his own team record for shutouts a season.
The Senators have a league-best 86 points.
Minnesota, which is opening a three-game road trip, had lost three games in a row before posting a 3-1 triumph over St. Louis on Sunday.
Antii Laaksonen had two assists and Manny Fernandez recorded 21 saves in the win.
The Wild, who had 12 road wins all of last season, already have 12 this campaign.