The Cavaliers made 53.1 percent of their field goals, including 48.1 percent from beyond the arc, led by guard J.R. Smith's season-high 27 points.
"He has the ability to go for 15, 17 in a quarter," Cavaliers forward LeBron James said. "Tonight was one of those instances where every time he got the ball, we wanted him to keep taking (shots)."
The victory extended the Cavaliers' winning streak to six games as Cleveland moved to 2-0 on its season-long, six-game road trip.
Forward Kevin Love, making his second trip back to Minnesota after a trade that sent him to Cleveland for Andrew Wiggins two summers ago, added 20 points and nine rebounds.
Wiggins led the Timberwolves with a career-high 35 points, the fifth time in his career he has scored at least 30 and the second time in three games against the team that selected him with the No. 1 overall pick in the 2014 NBA Draft.
"Pretty typical against us," Cavaliers coach David Blatt said. "(But) we were in control of the game. He can score all he needs to as long as we're winning the game."
Minnesota has lost four straight games and nine of its last 10 overall.
The Timberwolves used an early burst to build a seven-point lead four minutes into the game before Cleveland finally wore Minnesota down.
Smith was on fire from the start, nailing his first six shots before a miss that appeared to hit a fingertip on the way to the basket. He was 8 of 9 from the field in the first half, including 5 of 6 from beyond the arc as the Cavaliers led 62-46 at halftime.
"I think the fact that Kyrie (Irving) has been playing really helps because he's drawing so much attention and the floor opens up," Blatt said.
Wiggins was one of the few reliable sources of offense for Minnesota, hitting 8 of 10 from the floor with 21 points at the break.
"When he plays against guys like LeBron, we're not concerned about him showing up," Wolves interim coach Sam Mitchell said. "What we tell our young guys about is that they have to approach every game like they're playing San Antonio or Golden State or Cleveland, the upper-echelon teams. You just have to."
The Cavaliers pushed their lead to 21 points in the third quarter before the Timberwolves went on a 15-7 run. Minnesota, which made just two 3-pointers in the first 2 1/2 quarters, drilled four straight during the run to narrow the deficit to 13 points at 83-70.
Cleveland finished the quarter on a 12-4 run, sparked by back-to-back 3-pointers by Love and guard Iman Shumpert, to take a 19-point lead into the fourth quarter.
"We had good ball-movement, good shots ... They're just more experienced," Mitchell said. "They're deep, they're physical, they're big. They have three legit All-Stars, then you've got Shumpert and J.R. Smith and (Timofey) Mozgov and you just go on."
Cleveland built on that run to start the fourth quarter, extending its lead to 27 points with 7:35 to play.
James was mostly quiet offensively, scoring 13 points, but had 12 rebounds and eight assists in 32 minutes.
Four Cavaliers starters finished in double figures. Shumpert had 23 points off the bench and guard Kyrie Irving added 13 points.
"I thought he played simple and straight," Blatt said of Shumpert. "He didn't have to play outside himself. (He) just knocked down his shots and made good decisions on when to shoot."
Timberwolves rookie center Karl-Anthony Towns had 22 points and six rebounds. Forward Shabazz Muhammad has also had 22 points in 26 minutes coming off the bench.
NOTES: Cavaliers G Mo Williams revealed he has partially torn ligaments in his right thumb after flying to New York on Thursday for a second opinion. Williams hasn't played in Cleveland's last three games but is available to play while the thumb heals. ... Timberwolves G Tyus Jones and F Damjan Rudez were inactive. ... Cleveland continues its six-game road trip against the Philadelphia 76ers on Sunday at Wells Fargo Center. Minnesota plays the Dallas Mavericks on Sunday in the third of a four-game homestand.