Tony Arata and Larry Henley were also celebrated at the Tennessee ceremony, and Yearwood was full of praise for her pal Carpenter.
Carpenter, who is only the 14th female inductee of all 188 members, was overwhelmed by the tribute, and declared, "I know that I stand on a lot of shoulders just to get to this place. I'm just so happy."
Brooks sang New Way To Fly, Papa Loved Mama and Three Wooden Crosses to Williams during an induction speech, which came a year after his own entry into the Hall of Fame.
He said, "I cried the whole time and I'm going to cry all night tonight, too, but now it's for one of your brothers. I think I'm more excited for Kim and Tony going in. For me it's long overdue."