Williams, who took three different teams to the World Series, died on Thursday at his home in Las Vegas at the age of 82.
Williams was the Padres manager during the 1984 World Series against the Tigers, when Gibson was Detroit's starting right fielder.
In the deciding Game 6, Gibson strolled to the plate in the bottom of the eighth inning with two men on base and the Tigers leading, 5-4. Gibson had homered earlier in the game and Williams visited the mound to chat with reliever Goose Gossage. Williams wanted to intentionally walk Gibson, but Gossage talked the manager into letting him pitch to Gibson. The decision backfired, though, and Gibson launched a three-run home run that clinched the series for Detroit.
"Maybe that should be a lesson to me as a manager," Gibson said on Thursday.
Gibson has fond memories of the 1984 World Series and had nothing but high praise for Williams prior to Thursday's game against the Cardinals.
"He was certainly a quality individual for the game of baseball," Gibson said. "He's given a lot to the game."