The evening honored the health care workers who supported the couple during the birth and passing of their daughter, Sterling Sol.
During the game, Vesia thanked the group of health care workers, greeting them with hugs on the field. They all wore custom T-shirts with the Dodgers logo and Sterling's initials.
Vesia was taken off the roster ahead of the World Series in late October, with his wife, Kayla, due to give birth. Their daughter died two days later.
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During a postgame interview, a reporter asked how meaningful the night was for Vesia and his wife.
"I'm going to cry man. It's a very emotional day," he said. "Everybody up there played a very, very big part. Kay and I are just so happy to able to at least share today ... it's unbelievable."
Tuesday marked the first time Vesia had seen the health care staff since October.