The 49ers advanced to a home NFC championship showdown against either the Seattle Seahawks or Green Bay Packers with a relentless defensive display to throttle the Vikings offense led by quarterback Kirk Cousins.
Cousins, the hero of last week's upset over the New Orleans Saints, was given a torrid time, sacked six times by a rampant Niners defense.
"I was pumped for the defense," said 49ers head coach Kyle Shanahan.
"When you see how well the defense is playing it makes it so much easier. I think our whole team fed off it.
"Our defense just kept getting us the ball back. It was a great overall win for the whole team."
San Francisco got off to a dream start after forcing Minnesota to punt on their opening possession in front of a packed house at Levi's Stadium in Santa Clara.
Garoppolo then marched the 49ers 61 yards upfield on a smooth, eight-play opening drive that culminated with the San Francisco quarterback picking out receiver Kendrick Bourne with a three-yard pass for a touchdown.
The Vikings hit back immediately, leveling the score on their next possession when Cousins floated a superb pass just beyond 49ers cornerback Ahkello Witherspoon to find Stefon Diggs for a 41-yard touchdown.
That was as good as it got for the Vikings offense, however, although the 49ers benefited from a slice of fortune to regain the lead.
The replay booth came to San Francisco's rescue, however, correctly spotting that Samuel had a knee down before the fumble occurred.
Buoyed by that break, the 49ers advanced to the one-yard line, where running back Coleman skipped over for the go-ahead score at 14-7.
Minnesota's defense came up big to keep their team in touch, Kendricks reading Garoppolo's attempted pass to Samuel to pluck the interception deep in Niners territory.
Minnesota were unable to make the most of the turnover, though, settling for a field goal to go in 14-10 down at half-time.
San Francisco dominated the second half, extending their lead to 17-10 in the third quarter with a 35-yard Robbie Gould field goal and then exploiting a Richard Sherman to set up Coleman's second touchdown for a 24-10 edge.
Gould added his second field goal from 21 yards to make it 27-10 and complete the scoring at the start of the fourth quarter.