Anthony Edwards top-scored with 40 points – 31 in the second half – and also had nine rebounds.
Karl-Anthony Towns added 28 points and 10 rebounds for Minnesota while Jaden McDaniels had 18 points.
The victory came despite big efforts from Suns duo Devin Booker and Kevin Durant. with Booker scoring a play-off career-high of 49 points and Durant adding 33.
Minnesota will face either the Denver Nuggets or the Los Angeles Lakers in the Western Conference semi-finals.
They had to complete the game without coach Chris Finch – the former Sheffield Sharks boss had to be helped off the court for treatment with one minute and 41 seconds left after being run into by his own player Mike Conley.
Elsewhere, the Indiana Pacers eased to a 126-113 win over the understrength Milwaukee Bucks to go 3-1 up in their Eastern Conference first-round tie.
The Bucks were already without injured stars Damian Lillard and Giannis Antetokounmpo and had Bobby Portis ejected early on.
Myles Turner scored 29 points and Tyrese Haliburton added 24, despite being a doubt for the game with a back problem.
The Los Angeles Clippers held off an epic fightback from the Dallas Mavericks to win 116-111 and level their Western Conference series at 2-2.
The Mavericks were down by 31 points in the first half, but, inspired by Kyrie Irving’s 40 points, took the lead before the Clippers regained control in the final minutes.
James Harden and Paul George starred for the Clippers, scoring 33 points each.
Had the Mavericks won, they would have matched the play-off record for the biggest comeback win the Clippers set against the Golden State Warriors in 2019.
Mavericks star Luka Doncic recorded the only triple double of the match, scoring 29 points, 10 rebounds and 10 assists, but it was in vain.
Game five of the first-round series takes place in Los Angeles on Wednesday.
Elsewhere, the New York Knicks beat the Philadelphia 76ers 97-92 to take a 3-1 lead in their Eastern Conference series.
Jalen Brunson starred for the Knicks, scoring 47 points and recording 10 assists as his side bounced back from defeat in game three.
Brunson’s exploits also saw the American become the first player in franchise history to post at least 30 points and 10 assists in consecutive play-off games.
