Williams added three blocks and Joe Coleman had 16 points, five rebounds and three steals for the Gophers (15-5, 3-4).
"I can feel us gaining confidence with each win," said coach Tubby Smith, whose Gophers appeared to be dead in the water after consecutive home losses to Iowa and Purdue dropped them to 0-4 in the conference.
John Shurna scored 21 points for the Wildcats (12-7, 2-5), but he shot just 8 of 21 and scored 10 of those points in the final 11 minutes with the game already decided.
Northwestern shot 32.7 percent and missed its first 15 shots of the game to lose for the fourth time in five games. Drew Crawford, the Big Ten's third-leading scorer at 17.6 points per game, managed just five points on 2 for 10 shooting.
"Everything was off," Wildcats coach Bill Carmody said. "I don't know what to say, to tell you the truth." Ralph Sampson III had 10 points and six rebounds and Julian Welch added 14 points and five assists for the Gophers. Minnesota shot 57.7 percent and had 10 steals as it tries to stay in the NCAA tournament discussion without star Trevor Mbakwe, who is out for the season with a knee injury.
Wins at Indiana and Penn State and now at home against Northwestern have steadied the Gophers after such a rocky start.
"Just be aggressive and go at teams," Coleman said. "We started out slow and we kind of just were playing not to lose. We have to start playing to win and going out and taking teams down like we are supposed to do and not let them attack us first."
The Wildcats won 10 of their first 11 games, raising hopes that they would make the NCAA tournament for the first time in the program's history. They have victories over Georgia Tech and No. 9 Michigan State on their resume, but an ugly loss like this one certainly won't help them.
"They've won three in a row and found out a way to start winning," Carmody said of the Gophers. "That's what we have to do."
Minnesota came out aggressively on defense, attacking Shurna from all angles to get the precise Wildcats offense off track. Crawford and Shurna couldn't buy a basket for most of the first 20 minutes, shooting a combined 5 for 18 in the first half.
The Gophers scored the first 11 points of the game. Northwestern didn't get on the board until Davide Curletti scored on a layup almost nine minutes into the period.
Williams' combination of size and athleticism gave Shurna fits, forcing him into taking shots at awkward angles and completely flustering him. Williams blocked Shurna's layup on the first possession of the game, and it didn't get any easier for a player who entered the day tops in the league with 19.1 points per game.
"I felt like Rodney did a great job on him and made him frustrated in the first half," Welch said. "He got a few open buckets at the end of the game, but Rodney did a great job on him."
Shurna missed his first seven shots and didn't get on the board until Tubby Smith sat Williams down well over halfway into the period. With Oto Osenieks on him, Shurna forced a switch to center Elliott Eliason and spun past him for a layup and his first field goal.
Smith immediately went back to Williams, giving Osenieks an earful as he headed to the bench.
The Gophers hummed along on offense as well, with Coleman's steal and dunk in transition giving them a 36-14 lead with just over three minutes to play in the first half.
They led by 22 again eight minutes into the second half against Northwestern's porous defense, and only then did Shurna get going. He hit a 3 and scored on two driving layups, but by then it was too late. He even stepped over the line on a free-throw attempt in a sign of just how the day went for him.
"No excuses for the missed free throws," said Shurna, who went 2 for 8 from the line. "As a senior, it's my job to step up. I didn't do that. I take full responsibility for that. We have to play a lot better."