Booker and Warren each scored 35 for Phoenix, whick snapped a five-game losing streak and won for the first time in four tries on a season-long, six-game homestand.
The duo combined for 22 of the team's 33 points in the fourth quarter and almost all of the big ones. They combined to make 28 of 44 shots as Phoenix shot 54.1 percent.
In a game punctuated by huge runs on both sides, the Suns trailed 103-97 after Jeff Teague capped a 9-0 Minnesota run with a 3-pointer with 4:46 left. But Booker had seven points and Warren four over the next 3:55, and when Booker fed Marquese Chriss for a 3-pointer in the corner, the Suns had a 111-103 lead and control of the game.
Andrew Wiggins scored 27 points and Jimmy Butler added 25 for the Timberwolves (7-5), who missed a chance to start the season with eight wins in their first 12 games for the just the third time in team history. Karl-Anthony Towns (17 points, 12 rebounds) and Taj Gibson (16 points, 11 rebounds) both added double-doubles.
Minnesota missed 15 of 24 shots in the first quarter but nine made free throws and a late 11-2 run gave them a 28-19 lead. Wiggins had eight points and Butler seven for Minnesota.
Booker had 12 points in the second quarter and his third 3-pointer of the quarter pulled Phoenix to within 57-56 with 38.6 seconds left. But he fouled Butler on a 3-point shot with less than a second left.
Butler, who was a perfect 10-for-10 from the line in the first half, gave Minnesota a 60-56 lead at the half.
The Suns jumped out with a 15-5 run back-to-back Warren baskets giving the Suns their biggest lead at 83-75 with 4:06 left in the third. But Minnesota regrouped and closed the quarter on a 12-2 spurt to take an 88-85 lead to the fourth. Butler had 10 points in the quarter.
NOTES: Suns F Jared Dudley will miss one to two weeks after suffering a bone bruise during the loss to the Orlando Magic on Friday. ... C Tyson Chandler returned after missing two games to back spasms and G Tyler Ulis made his first start of the season. ... The game featured former Kentucky teammates and the two highest scoring players of the 2015 Draft -- Minnesota C Karl Anthony Towns (3,815 points) and Phoenix G Devin Booker (3,086). ... Minnesota has only started better than 8-4 once in franchise history, going 10-2 to begin the 2001-02 season.