Canada's Wiggins finished with a game-high 41 points for the Timberwolves, equalling his second-highest point total this NBA season.
James also had 14 assists for Cleveland, who sealed their 38th win of the season with 1:39 remaining when ex-Timberwolves player Derrick Williams finished off a fast break layup.
The layup came just moments after James had nailed a step back three pointer.
Wiggins got the Timberwolves back in the game Tuesday, sparking a rally after Irving hit a three pointer halfway through the third quarter to give Cleveland a 14-point lead.
Wiggins tallied 19 points in the third quarter,
Cleveland had to make due without forward Kevin Love, who had surgery on his left knee on Tuesday and will be sidelined for six weeks. Love was averaging 20 points and 11 rebounds per game.
- No Love, no problem -
"The one thing that we can always rely on is the fact that we've played without Kev before," James said. "We've had to do that in the playoffs. As much as you don't like to play without some of your big guns, sometimes if it happens then you're just ready for it."
Williams is on a 10-day contract with Cleveland after previously playing for the Miami Heat this season. His teammates spoke highly of his performance Tuesday.
"He plays extremely hard, plays above the rim. He can guard two through almost five," Irving said. "Then when you have the ability to do that and you're on a team like this, we're going to get you the ball and we're going to put you in a spot to be successful on both ends."
This is the Cavaliers' second win over Minnesota in a two-week span. The Cavaliers crushed the Timberwolves 125-97 on February 1.
Butler, who last played February 10 and was sidelined with a right heel contusion, nailed seven free throws in the final 1:48.
He played 38 minutes and hit 15 of 19 free throws as the Bulls snapped a three-game losing streak. He was two for 10 from the field. Doug McDermott scored 20 points for the Bulls.
In Los Angeles, DeMarcus Cousins scored 40 points, grabbed 12 rebounds and dished out eight assists, leading the Sacramento Kings to a 97-96 victory over the Los Angeles Lakers at Staples Center arena.
Sacramento improved to 24-32 and defeated the Lakers for the fourth straight time at Staples Center.