Johnson scored a season-best 19 points, had 11 rebounds and held Minnesota's Kevin Love to 13 points on 3-for-16 shooting as Toronto downed the Timberwovles 97-87.
Johnson said it was a matter of being aggressive.
"I know (Love) goes crazy on the boards," Johnson said. "So I pretty much tried to shut him down, face guard him and just try to get him out of his groove. I think I frustrated him a little bit tonight."
It was a good game for Johnson, especially since he was suffering from allergies.
Love entered the game averaging 25.4 points a game on 47.1 per cent shooting with an NBA-best 15 rebounds a game. He can also hit three-pointers, hitting five in six attempts against Dallas on Jan. 1.
"He had just had one of those nights," Raptors head coach Dwane Casey said, "(Love) is one of the top power forwards in the league. He is a great passer, he sees the floor and he is a heck of an offensive rebounder. He had one of those nights. Amir did an excellent job on him.
"I think our guys did an excellent job of sandwiching him in and keeping a body on him."
Andrea Bargnani, who led the Raptors with 31 points, agreed with Casey.
"I think Amir did an unbelievable job on Love," said Bargnani. "He really got him out of the rhythm and he shot the ball really bad. It was great defence. Everybody made an extra effort."
The scoring by Bargnani and the defensive work by Johnson and others helped Toronto (4-5) maintain its dominance of Minnesota (3-6). The Raptors have won 14 of their past 15 games against the Timberwolves, including eight in a row at Air Canada Centre.
Minnesota has not won in Toronto since Jan. 21, 2004.
Overall, the Timberwolves shot just 33.8 cent on the night while the Raptors shot 44.2 per cent. Toronto also blocked nine shots, four by James Johnson.
"I thought we were way too inconsistent during the course of the game and it cost us," said Timberwolves head coach Rick Adelman. "We got down by 12, made a nice comeback, but down the stretch we didn't defend them well enough and we didn't execute well enough."
Bargnani also had nine rebounds for Toronto. Jose Calderon added 14 points and six assists and Leandro Barbosa chipped in with 13 points off the bench.
The Raptors played the first of three games on back-to-back-to-back nights. They will play five games in six nights. It will be the only time Toronto plays on three successive days this season.
J.J. Barea led Minnesota with 16 points while Luke Ridnour and Derrick Williams scored 13 each and Ricky Rubio added 10.
The Timberwolves played the second of their run of back-to-back-to-back games.
The 21-year-old Rubio is a friend and fellow member of Spain's national team with Calderon. Rubio is still being used from the bench and he has made an impression early in his first NBA season.
Calderon used that familiarty against the younger Spaniard.
"It's hard to guard him," said Rubio. "He is smart, tough to play and he showed us one more time he is a great point guard here in the NBA. He controlled the tempo of the game. He scored two shots at the end of the game to kill us."
Calderon praised Toronto's tough forwards for their ability to stop Minnesota's offence.
"The defence was great today," Calderon said. "Amir (Johnson) and James (Johnson) and all the big guys who had to guard Love tonight were great."
The Raptors, who were coming of two lacklustre losses — at home to New Jersey and away to Philadelphia — took a four-point lead into the fourth quarter.
But Minnesota scored the first four points of the fourth to pull even. Then Barea hit a three followed by a layup from Williams to put the Timberwolves ahead 78-75.
The game was tied at 80-80 after Bargnani scored on a driving reverse layup with 6:35 to play. There was no more scoring until Amir Johnson put in the rebound after Bargnani missed a 17-foot jumper to give the Raptors an 82-80 lead with 3:16 to play.
Calderon and Bargnani extended Toronto's lead to six points with under two minutes to play put the game out of Montreal's reach.
Notes: Attendance at Air Canada Centre was 14,097. ... Raptors centre Aaron Gray underwent an ablation procedure on Wednesday to correct recurring episodes of a rapid heart rate. He is expected to be able to return to the court in two weeks. .... Toronto guard Jerryd Bayless missed his sixth consecutive game with a sprained left ankle. .... Minnesota won at Washington on Sunday to end a 12-game road losing string. The Timberwolves were playing just their third road game of the season Monday.