"We got a little complacent out there with a 27-point lead, and they (Stanford) made some adjustments to the option," said Williams, who sparked the Atlantic Coast Conference champion Tigers to a 27-0 halftime advantage.
Ford, who coached his first collegiate game here eight years ago in a celebrated 17-15 victory over Ohio State in Woody Hayes' final game, said he was happy the team may have learned an important lesson without having to lose.
"They came close to making us believers," Ford said. "We need to learn how to put people away."
Clemson's 27-0 halftime lead and domination of the first 30 minutes had observers thinking North Carolina's 35-0 rout of Air Force in 1963 might be endangered as the most one-sided game in the 42-year history of the Gator Bowl.
Clemson (8-2-2) rolled up 291 yards on offense and 15 first downs in the first half, and Stanford could manage just 57 yards and three first downs.
Clemson built a 24-0 lead by the time Stanford (8-4) managed its initial first down midway through the second period.
"It was a quiet halftime locker room," said Stanford's Brad Muster, who scored all three Cardinal touchdowns in the final half. "Once things got started, we finally realized where we were at and played a little with pride."
Muster, who shared Most Outstanding Player honors with Williams, got the Cardinal on the scoreboard with a one-yard touchdown run midway through the third period and caught a pair of scoring passes from Greg Ennis, covering 13 and 36 yards, in the fourth quarter.
"We didn't roll over and die," said Ennis, who hit on 20 of 40 attempts for 168 yards in his first collegiate start.
Williams, Chris Lancaster and Ray Williams ran for touchdowns and David Treadwell added three extra points kicks and a pair of field goals for Clemson.
"They just couldn't stop our option in the first half," said Williams, who passed for 101 yards in the first half.
Two other Stanford scoring drives died in the final period when Ennis was intercepted inside the 10, and when he missed an open receiver on fourth down with just over a minute left.
Stanford was without regular quarterback John Paye, who underwent surgery for a shoulder injury Monday, and starting linemen Tony Leiker and John Zentner--who didn't make the trip after testing positive for steroids in an NCAA drug test.
Muster rushed for 70 yards in 17 carries and caught 4 passes for 53 yards.
Terrence Flagler gained 82 yards in a dozen carries for Clemson, which finished with 244 yards rushing.
The victory gave Clemson a 7-6 record in bowl competition and a 3-2 Gator Bowl mark.
Stanford, 7-6-1 in bowl games, lost for the first time in 34 years in postseason play after four straight bowl victories.