The Spurs arrived in Minnesota with a 3-2 lead in their best-of-seven semifinals, and led throughout a victory that sets up a tantalising showdown series with the reigning champion and top-seeded Oklahoma City Thunder.
Stephon Castle led Friday's wire-to-wire win with 32 points and 11 rebounds, shooting 11-of-16 from the field, ably backed up by De'Aaron Fox and French superstar Victor Wembanyama, who added 21 and 19 apiece.
It is the first time a revitalised San Antonio has reached the conference finals since 2017. While the Thunder are heavy favourites for another championship, the dangerous Spurs enjoyed a 4-1 record against Oklahoma City in the regular season.
"We don't really care about the outside noise. We knew that we were ahead of schedule, probably in December of last year," said Castle.
"We know it's going to be tough to knock them off, but I think we're pretty confident we can do it," he added.
The Spurs got off to a fantastic start, tearing ahead in the first quarter, dominant in the paint and led by a rampant Castle.
Just when it was looking ugly for the Timberwolves, they fought back, their aggression spearheaded by star man Anthony Edwards.
But from a 74-61 half-time lead, the Spurs roared clear in the third quarter, successfully double-teaming Edwards to shut down Minnesota's most potent threat.
By the end of the third quarter, San Antonio enjoyed an insurmountable 26-point lead, their 56% shooting accuracy far outstripping the opposition.
At a timeout with eight minutes remaining, a 25-point deficit on the board, and both teams preparing to send out their benches for the remaining minutes, Edwards walked over to pre-emptively congratulate the Spurs on their resounding win.