Williams made six three-pointers as he set a new franchise points record and also reached the highest NBA match total so far this season as the Timberwolves won 110-101.
Minnesota were 75-69 down going into the final quarter but a mammoth 41-point haul in the final 12 minutes turned it around to give the Timberwolves only their sixth win this year.
Like the Timberwolves, the Washington Wizards got a considerable monkey off their backs as they beat the San Antonio Spurs for the first time since 2005.
John Wall led the charge for Washington with 25 points and eight assists as they won 101-93, while his opposite number Tony Parker top-scored for the Spurs with 14 on a disappointing night for the reigning champions.
LeBron James chipped in with 33 points on his return from injury for the Cleveland Cavaliers, but he was eclipsed by Markieff Morris whose 35-point haul helped the Phoenix Suns to a 107-100 victory at US Airways Center.
Al Horford notched a triple double, with 21 points, 10 assists and as many rebounds, as the Atlanta Hawks claimed a ninth win on the bounce with a 105-87 triumph over the Philadelphia 76ers at the Wells Fargo Center.
Elsewhere, the Golden State Warriors edged the Utah Jazz 116-105, the Dallas Mavericks squeezed past the Sacramento Kings 108-104 in overtime and a 19-point haul from Mario Chalmers helped the Miami Heat come out on top 78-75 against the Los Angeles Lakers.