Markieff Morris stole the ball allowing Bledsoe to score on a driving layup and snap a tie game in front of a crowd of 17 866 at the Target Centre arena.
Phoenix was down by as many as 22 points in the first half and trailed 103-93 entering the final quarter of the National Basketball Association game.
Bledsoe tallied nine points and PJ Tucker had eight in the fourth for the Suns, who rallied to post their fifth victory in six contests.
Bledsoe finished with 21 points while Morris shot 10-of-13 from the field and had 25 points. Tucker tallied 19 points and Goran Dragic chipped in with 18.
Kevin Love paced the Timberwolves attack with 36 points, 14 rebounds and nine assists. Love also had a key turnover in the final minute of play.
Kevin Martin scored 25 points for Minnesota who lost consecutive games for the first time since the all-star break.
Minnesota led by 10, 103-93, at the end of the third quarter.
Dragic drained a three pointer with just over seven minutes left to give Phoenix their first lead, 107-106, since the early portion of the game.
Minnesota fought back but Dragic set up Tucker for a score from in close to tie the game with 66 seconds left.
Love then had the ball stripped by Morris, leading to Bledsoe’s go-ahead layup for a 120-118 Phoenix lead.
Minnesota’s next run down the court ended in Love missing a three-point attempt, and Bledsoe and Tucker combined to hit four free throws to cap the rally and clinch the victory.