"I feel like I've been a little bit more consistent lately," Williams said. "The guys have been giving me the ball in the right spots. I was feeling good."
Minnesota (21-14) advances to the quarterfinals at Middle Tennessee on Wednesday night. The Blue Raiders defeated Tennessee earlier Monday.
The Gophers expanded a 35-23 lead at halftime with a 15-2 spurt early in the second half. Andre Hollins hit consecutive 3-pointers and Andre Ingram's putback with 12:22 remaining ended the surge and gave Minnesota a 56-33 lead.
"We came ready to play," Minnesota coach Tubby Smith said. "Rodney got us off to a good start. We had some guys step up who hadn't played a lot."
Hollins and Joe Coleman finished with 14 points each for the Gophers.
Rion Brown scored 16 points for Miami (20-13).
"We started the game very lethargic," Miami coach Jim Larranaga said. "We never seemed to be able to generate any defensive intensity."
The Gophers shot 58 percent as they converted 28-of-48 shots and out-rebounded Miami 41-26.
Minnesota reserve forward Oto Osenieks favored the back of his head and collapsed on the court after colliding with Miami's Reggie Johnson 1:10 into the second half.
The freshman from Latvia never lost consciousness and quickly reached his feet. Osenieks watched the rest of the game from the Minnesota bench.
"He's fine now, he had a dizzy spell," Smith said.
Minnesota had its second double-digit lead of the first half after a 13-2 spurt. Williams had two three-point plays and Coleman's jumper with 4:46 remaining capped the run and gave the Gophers a 26-15 lead.
After Reggie Johnson scored consecutive baskets and helped cut Minnesota's lead to 26-20, the Gophers outscored the Hurricanes 9-3 in the final 2:49 of the first half and led 35-23 at halftime.
Minnesota shot 14 of 23 from the field in the first half.
The Hurricanes rallied from a 12-0 deficit and scored 11 unanswered points during a 2:49 span early in the first half. Garrius Adams' steal and breakaway dunk with 10:54 ended the surge and got the Hurricanes to within 12-11.
The Gophers kept Miami scoreless for the first 6:15.
"I have no clue why we came out like that," Brown said. "I can't explain it."
Miami missed its first seven shots until Trey McKinney Jones' jumper with 13:45 ended the early scoring drought.