The loss at Chicago's Soldier Field was the Bears' fourth consecutive setback since the team started the season with a 5-2 record.
Cousins completed 25 of 36 passes for 292 yards, two scores and an interception in the victory. Bears quarterback Nick Foles completed 15 of 26 passes for 106 yards and an interception before he left the game due to a foot injury in the final minute.
The Vikings and Bears each began the game with turnovers. Minnesota tight end Kyle Rudolph fumbled on the opening drive and Foles threw an interception to safety Harrison Smith two plays later.
Cousins then completed a 17-yard touchdown to Adam Thielen to give Minnesota an early edge. Bears kicker Cairo Santos split the uprights for a 23-yard field goal on Chicago's next drive to make the score 7-3 at the end of the first quarter.
Bears linebacker Khalil Mack intercepted Cousins at the two-minute warning of the first half and Santos made a 42-yard kick on the resulting drive to cut the Vikings lead to one point at halftime.
The Bears carried that momentum into the second half when special teams ace Cordarrelle Patterson scored on a 104-yard kickoff return to give Chicago a 13-7 lead.
Vikings kicker Dan Bailey made field goals on two of Minnesota's next three drives to tie the score at 13-13 heading into the fourth frame.
The Vikings continued to play strong defense and added a 9-play, 73-yard scoring drive to start the fourth quarter. Cousins connected with Thielen to end the 4:43 possession and give Minnesota the final 19-13 advantage, with 10:10 remaining.
Neither team scored for the rest of the NFC North showdown.
Theilen had 63 yards and two scores on four receptions for the Vikings. Rookie wide receiver Justin Jefferson had eight grabs for 135 yards in the win. Minnesota running back Dalvin Cook had 96 rushing yards and 16 receiving yards.
"Obviously, we struggled mightily on offense in having the four three-and-outs in the second half," Bears coach Matt Nagy said. "We had field position. We couldn't convert on that in the red zone.
"It overshadows how well I thought our defense played and the different sudden changes they had, how well our special teams played. I was proud of those guys. So two out of the three parts right now are playing well. [That has] been a constant theme for us."
The Bears (5-5) have a bye week before they face the Green Bay Packers in another NFC North game at 8:20 p.m. EST on Nov. 29 in Green Bay, Wis. The Vikings (4-5) next host the Dallas Cowboys at 4:25 p.m. EST on Sunday.