Thomas Robinson had 14 points and a career-high 18 rebounds for Portland, which won its second straight after a three-game slump.
Kevin Love scored 31 for Minnesota, which had won three in a row. It was Love's franchise-best fifth straight game with 30 or more points.
The Blazers played without All-Star forward LaMarcus Aldridge, who missed his third straight game with a groin injury.
After trailing by as many as 18 points in the first half, Nicolas Batum's fast-break layup gave Portland an 84-80 lead going into the fourth quarter.
It was more of the same as the Blazers continued to attack. Robinson, who sparked the second-half comeback, blocked Corey Brewer's shot on one end, Claver grabbed the rebound and Will Barton broke free for a dunk that gave Portland a 92-83 lead.
Lillard's 3-pointer made it 105-91 with 4:14 left, and Timberwolves coach Rick Adelman took Love out with 3:36 to go.
The Timberwolves were coming off a 121-104 victory at Utah on Saturday night. Love led the way with 37 points, 12 rebounds and 10 assists for his first career triple-double.
Love presented a significant matchup problem for the Blazers with Aldridge sidelined by a left groin strain.
Aldridge wasn't the only Blazer hurting: The team was also without forward Joel Freeland because of a right knee sprain and center Meyers Leonard because of a left ankle sprain.
Love finished with 10 rebounds.
The Timberwolves continued to miss center Nikola Pekovic because of a sore right ankle and Kevin Martin because of a fractured bone in his left thumb.
Love got off to a fast start with seven points as the Timberwolves built an early 18-9 lead. By the end of the opening quarter, Love had 13. Minnesota extended the lead to 43-28 early in the second quarter on Shabazz Muhammad's short jumper.
The Timberwolves stretched the lead to 52-34 after a short jumper and a pair of free throws from J.J. Barea.
Portland then got back into the game with an 18-8 run capped by Robinson's two layups and Nicolas Batum's 3-pointer, closing the gap to 60-52 at the half.
A pair of 3-pointers from Lillard and Batum put Portland in front 74-73. It was short-lived and Love drained a 3 to give Minnesota an 80-76 lead before the Blazers' furious fourth-quarter surge.
Portland was coming off a 102-94 victory over the Jazz on Friday night. Lillard had 28 points, including 14 in the fourth quarter.
NOTES: Love is from Lake Oswego, just outside of Portland. ... Adelman coached the Blazers from 1989-94, guiding the team to two Western Conference titles. ... Love has at least 25 points and 10 rebounds in 10 straight games, the longest run of 25-10 games since Shaquille O'Neal had 13 in a row in 2001. ... Love has an NBA-high 47 double-doubles.