The Kings trailed by 11 in the third quarter and were down 82-81 before going on an 11-2 run to go in front for good. Cousins, who had his eighth straight double-double, started the surge with a thunderous dunk and McCallum followed with his 3s, one from the left corner and the other from the right.
Cousins was hit with a technical foul with less than 2 minutes remaining, his 16th of the season. By NBA rules, he must sit out Sacramento's final regular season game.
Kevin Love had 43 points and 11 rebounds for Minnesota after sitting out Friday's 112-110 win over Houston because of a hyperextended right elbow.
The Timberwolves lost after leading 62-51 with eight minutes left in the third in what might have been former Kings coach Rick Adelman's final appearance at Sleep Train Arena. The 67-year-old Minnesota coach remains a beloved figure in the state's capital, having guided the Kings from 1998-2006. Sacramento made the playoffs in each of his eight seasons and haven't been back since.
Adelman clearly has fond memories of those glory days in Sacramento and he's been back numerous times as a visiting coach as well.
This game, however, might hold special significance since it might be Adelman's last. He has taken time away from coaching each of the past two years to take care of his wife, Mary Kay, who has had health problems. Speculation around the NBA now is that Adelman will step away for good at the end of the season.
The Timberwolves pulled to 100-98 with 1:13 left to play on three free throws by Love after Cousins was charged with the technical foul. Cousins then drove the baseline and dunked with 24.2 seconds remaining, helping Sacramento end a five-game losing streak while evening the season series with Minnesota.
J.J. Barea missed a 3-pointer and Love was off on a 16-foot jumper in the final 20 seconds for the Wolves.
Minnesota trailed by 11 early before going on a 12-0 run in the second quarter capped by Dante Cunningham's three-point play that put the Wolves up 40-32.
Love finished the half with 13 points, including two free throws to give Minnesota a 52-47 halftime lead.
The Timberwolves extended their lead to 62-51 with 8:03 left in the third, then Sacramento went on its big run.
NOTES: Kings F Rudy Gay (lower back strain) sat out for the third time in four games. ... Cousins moved past Vlade Divac for eighth on Sacramento's career scoring list.