With the Marlins playing the Rays at Tropicana Field, Webb's family is able to attend the series.
The 26-year-old right-handed reliever is from Clearwater, Fla., and his parents will be at the game.
A graduate of Clearwater Central Catholic High, Webb came up big in the Marlins' 4-3 win in 15 innings on Saturday. The right-hander threw three innings of scoreless relief, and he was credited with the win.
Webb actually recorded the final out of the 14th inning at midnight.
"So I pitched on Father's Day," the right-hander said.
The Marlins also are off on Monday before facing the Red Sox at Fenway Park on Tuesday. So after Sunday's series finale with the Rays, Webb will spend time with his family.
"It means a lot," Webb said. "The fact that I can come to any city and have my family come watch is something everybody dreams of. We have a day off Monday, so I'll be able to stay and spend some time on Father's Day with them. It's really special."
Webb has a special relationship with his dad, because the two share something in common. Both have pitched in the big leagues.
Hank Webb was a 10th round Draft pick by the Mets in 1968. He saw action with New York from 1972-76, and he was with the Dodgers in 1977.
Hank appeared in 53 MLB games.
"I'll always have two pitching coaches, I can say," Ryan said. "Growing up, I was always the one prying him for information. He was never really pushing me to go out there and play baseball. I'd pitch in high school, and we'd go out after every single game and talk about pitching."
In 2004, the A's selected Webb in the fourth round. He was traded in 2009 to the Padres, and the Marlins acquired the right-hander, along with Edward Mujica, after the 2010 season for Cameron Maybin.
Webb has become a valuable late-innings reliever for the Marlins.
"After I got drafted, I called [my dad] every single day," Webb said. "It was just nice to always have somebody to talk to. To have somebody who has seen me every day, and watch me progress. He always has a lot of good information, and is a good influence. It's special to have him here."