Groulx entered the night with two goals in 68 career NHL games.
Morgan Rielly and Matthew Knies also scored for Toronto (29-27-12), which was coming off a 3-2 shootout loss at the Buffalo Sabres on Saturday but is 2-0-1 in its past three games. Anthony Stolarz made 36 saves.
Vladimir Tarasenko scored twice, and Ryan Hartman and Mats Zuccarello each had two assists for Minnesota (38-18-12), which has lost three straight (0-2-1), including 4-2 to the New York Rangers on Saturday. Jesper Wallstedt made 22 saves.
Rielly put Toronto ahead 1-0 at 1:07 of the second period. He chipped down from the point, took a cross-slot pass from Matias Maccelli, and roofed a shot short side over Wallstedt.
Groulx increased the lead 2-0 at 2:19, deflecting Troy Stecher's shot from the right point after Jeff Petry turned the puck over to Nicholas Robertson below the goal line.
Groulx made it it 3-0 at 8:18. He scored glove side from the top edge of the left circle after intercepting Matt Boldy's blind clearing attempt into the middle of the zone.
Tarasenko cut the deficit 3-1 at 4:51 of the third period, tapping in a pass from Zuccarello near the left post.
Tarasenko then made it 3-2 just 23 seconds later. He skated along the left boards and cut to the circle before scoring glove side with a low wrist shot through a screen.
Knies shot into an empty net after blocking a shot from Quinn Hughes to make it 4-2 at 19:23.
