Teams have until Saturday to reduce their rosters from the current 75-man limit to the 53-man limit for the regular season.
Williams, who ran more effectively than his mediocre stats indicated Thursday night, has been fighting through injuries to justify a roster spot.
The Cardinals used a 2011 second-round pick on Williams and had high expectations for him before a torn patella tendon ended Williams' rookie season in August of that year. Williams hasn't been able to stay on the field consistently since then. He took a step forward Thursday night in the preseason finale at Denver.
Arizona's plans at running back could evolve between now and the cutdown date Saturday, but for now, Williams' roster status appears secure.
In other news, Arians said veteran tight end Jeff King would undergo knee surgery Friday. Injuries are severely affecting depth at that position. Starter Rob Housler has a high-ankle sprain and might not be ready for the regular-season opener at St. Louis -- a concern for the Cardinals, who plan to use two tight ends extensively under Arians.