Williams' previous career high was 3.5 sacks in a Dec. 13, 2007 game against the Denver Broncos, when Williams was a member of the Houston Texans. The Bills' previous team record was four sacks, set twice by Bruce Smith, in 1990 and 1994, and once by Cornelius Bennett in 1987.
"I guess I am late," said Williams, who signed a six-year, $100 million contract with the Bills before last season.
Williams finished his injury-marred 2012 season with 10.5 sacks and was held without a sack in a season-opening loss to the New England Patriots.
"I don't think I've felt this way in the last five years," Williams said. "I finally feel like I am at peace, just as a person."
Williams called himself "one of the calmest persons you'll ever meet" but acknowledged his transition to Buffalo hasn't been as smooth as it could be.
"Just everything," Williams said when asked why he hadn't been "at peace" earlier. "Football is football, but you have a personal life and just life in general. My mind-frame and my demeanor is just totally different."
The Bills were able to keep consistent pressure on Panthers quarterback Cam Newton throughout their comeback win. Defensive lineman Marcell Dareus had a half-sack, while linebacker Kiko Alonso closed out the game with Buffalo's sixth sack.