Matthew Stafford was 19-of-31 passing for 209 yards and a two-point conversion through the air for Detroit (3-1), which pulled even with Green Bay in the NFC North.
Murray and Jerick McKinnon round out the Vikings running back depth chart behind Cook.
Dalvin Cook fumbled seven times, losing five, in final two years at Florida State.
The Vikings (2-2) lost more than just possession, when Cook limped off with an injury to his left knee and did not return.
Anthony Zettel had his second sack of the season in the second quarter. Matt Prater made FGs from 55 and 57 yards last week vs. Falcons, becoming second player in National Football League history with 10 career 55-plus yard makes; Raiders Sebastian Janikowski has 13.
NOTES: Detroit rookie LB Jarrad Davis missed his second straight game because of a concussion. A neck injury was added to the injury report in addition to the concussion and one or both will keep him out of action today.
Cook was ruled out for the remainder of Sunday's game. Another starter, OLB Paul Worrilow, limped off with a left knee injury on the defense's first play. But in addition the reactions of Cook and his teammates, this injury has a few things that nobody wants to see.
The Vikings play at Chicago on October 9, their second Monday night game in the first five weeks.