The Lions (1-3) have lost three straight, surpassing the longest skid by last year's playoff team.
Detroit has struggled with poor coverage on special teams.
The Lions are the first team since at least 1940 to give up a kickoff and a punt return for TDs in consecutive games, according to STATS LLC. They gave up scores on a kickoff and punt in last week's 44-41 loss in overtime at Tennessee.
Adrian Peterson had 102 yards rushing on 21 carries, running for more than 100 yards for the first time since Oct. 23, 2011.
Christian Ponder was 16 of 26 for 111 yards for Minnesota.
Jerome Simpson had four receptions for a team-high 50 yards and drew a pair of penalties to help set up scores. Simpson served a three-game suspension for violating the league's substance abuse policy.
On the first punt return of the second half, Sherels made Kassim Osgood miss and then wiggled through traffic and raced 77 yards for a TD that gave the Vikings a 20-6 lead.
Matthew Stafford was 30 of 51 for 319 yards without much help from teammates.
Brandon Pettigrew dropped a pass in the end zone, forcing Detroit to settle for a field goal and a 13-6 halftime deficit. Titus Young couldn't catch a pass thrown right to him on third down, leading to the Lions punting from Minnesota territory for the second straight time in the third quarter.
And, just when the Lions looked as if they were going to break through offensively, safety Jamarca Sanford forced Mikel Leshoure to fumble and recovered the ball at the Vikings 29 late in the third quarter.
Leshoure ran for just 26 yards on 13 carries after having 100 yards rushing in his debut last week.
Peterson helped Minnesota get in position to kick a field goal early in the fourth, but rookie kicker Blair Walsh missed from 46 yards after making his first nine field goals.
Detroit drove to the Vikings 7 on the ensuing drive and the possession ended when unblocked defensive end Everson Griffen sacked Stafford.
The Lions got right back down in scoring territory and didn't waste the opportunity with Stafford scoring on a 1-yard lunge, snapping the ball and extending it over the pile on a play that stood after video review with 2:56 left in the game.
Ponder connected with Simpson on a 27-yard pass on Minnesota's last drive and went to him again, but Bentley made a play to allow Detroit to get the ball back.
Vikings punter Chris Kluwe pinned Detroit on its 2 with 1:42 left and no timeouts and the drive was extended when Stafford's fumble was overturned by review because he was down before losing the football with 9 seconds left.
Stafford took the last snap from the Lions 44 and was sacked in a fitting end to a game dominated by Minnesota's defense and special teams.
Minnesota took a quick 7-0 lead on Harvin's kickoff return for a TD, starting toward the back left of the end zone, cutting across the field and sprinting up the sideline.
Pass interference penalties two on Detroit rookie Bill Bentley trying to cover Simpson set up the next three scores, all of which were field goals, and the Vikings led 13-3 midway through the second quarter.
Calvin Johnson had a shot to score late in the first half, but rookie safety Harrison Smith put a hit on him in the end zone that jarred the ball loose before Pettigrew dropped a potential TD to force Detroit to kick a field goal and settle for a 13-6 halftime deficit.