Senior Day was a smashing success at Miami.
"It's really why you come here," Williams said. "You come to The U to set records. You come to this place to do something no one else has done."
Will Mallory and Deejay Dallas also had touchdown catches for Miami (6-4, 4-3 Atlantic Coast Conference). Williams completed 15 of 22 passes for 253 yards, and the Hurricanes won their third straight.
"We felt like a performance like this was coming," Miami coach Manny Diaz said.
Louisville quarterback Micale Cunningham threw for two scores and ran for another, before he left injured in the second half. Hassan Hall had a 58-yard touchdown run for the Cardinals (5-4, 3-3) and running back Javian Hawkins had 105 yards on 15 carries.
Tutu Atwell had six catches for 142 yards, including an 80-yard touchdown on a catch-and-run for the Cardinals.
"We had a lot of things go wrong today," Louisville coach Scott Satterfield said.
Williams broke the single-game mark of five shared by six other Miami quarterbacks -- Bernie Kosar, Steve Walsh, Ken Dorsey, Brock Berlin, Kyle Wright and Stephen Morris. He also tied the single-game record for any ACC quarterback, done on seven other occasions.
"We didn't execute in a lot of areas," Hawkins said. "They did and it showed."
Dallas also ran for a score for Miami, which got touchdowns on each of its first four possessions -- the first time that's happened since a romp past Savannah State in 2013. Al Blades Jr. had a blocked punt and an interception for the Hurricanes and Murphy recovered a fumble on a muffed Louisville punt.
Murphy -- one of Miami's 13 seniors playing their final home regular-season game -- seemed to break the Hurricanes' "Turnover Chain" in that celebration. Turns out, it was only that the clasp came undone.
The chain is good as new. Right now, the Hurricanes feel the same way about their game. A team meeting when they were 3-4 led to accountability, and they're 3-0 since.
"I didn't know I had it. I was just filled with energy," Murphy said of the chain malfunction. "When they brought it out, I'm like `Oh my God, that's mine.' So I took it and I forgot I was wearing a helmet. I didn't break it. I hope I didn't."
Louisville: It was a costly day injury-wise for the Cardinals, who lost standout left tackle Mekhi Becton early with a left ankle injury. Becton returned to the sideline in street clothes, with a walking boot on the injured ankle.
Miami: The Hurricanes tied their record for points in an ACC game with 52, done on four other occasions. They did it without top tight end Brevin Jordan, who missed the game with an unspecified leg injury. Harley and Wiggins became the fourth Miami duo in the last 20 years to have multiple touchdown catches in the same game.
South Florida resident Jill Ellis, who guided the U.S. women's soccer team to the last two World Cup championships was in attendance and honored during an on-field ceremony.
Miami LB Shaquille Quarterman started his 49th consecutive game, tying Joaquin Gonzalez for the second-longest streak in school history. If he starts against FIU on Nov. 23, Quarterman will tie William Joseph's school record of 50 straight starts.
Louisville: Visit North Carolina State on Nov. 16. The Wolfpack have won the last two games in the series, which Louisville still leads 6-3.
Miami: After a third bye week this season, the Hurricanes play FIU at Marlins Park -- the former Orange Bowl site -- in Miami on Nov. 23.
More AP college football: https://apnews.com/tag/Collegefootball and https://twitter.com/AP-Top25
Jalen Hurts: In hindsight, transfer to OU 'happened for a reason'
Jalen Hurts said he would not have changed any decision or move from his college career, including his transfer from Alabama to play his final season at Oklahoma.
Former Florida quarterback Feleipe Franks shifts from SEC East to West, chooses Arkansas
Former Florida quarterback Feleipe Franks, injured last year during the Gators' resurgent season, will stay in the SEC, transferring to new-look Arkansas, joining new coach Sam Pittman.
Fulmer praises Joe Burrow, talks expanding CFP
Tennessee athletic director Phillip Fulmer discusses LSU's championship season and expanding the College Football Playoff on The Paul Finebaum Show.
Former Houston quarterback D'Eriq King ends speculation, transfers to Miami for senior year
D'Eriq King, who last week entered the NCAA transfer portal after playing four games for Houston last season, announced on social media Monday that he will transfer to Miami.
Titans DB coach Kerry Coombs to be Ohio State D-coordinator
Titans defensive backs coach Kerry Coombs is returning to his roots to be the defensive coordinator at Ohio State.
Best offense should be a good defense for resurgent Baylor under new coach Dave Aranda
Fresh off winning a national title at LSU as defensive coordinator last week, new Baylor coach Dave Aranda was introduced on Monday, promising to keep the Bears defense robust.