Skaggs, 27, was found dead at a Texas hotel on Monday.
Corbin normally wears No. 46 and was given the option to bypass the start by Nationals manager Dave Martinez, but he insisted on pitching.
“They came up together,” Martinez said before the game, according to MLB.com's Jamal Collier. “His best friend. He was emotional earlier, but he wants to pitch. He feels that’s what he needs to do.”
Corbin pitched well, tossing seven innings while allowing one earned run and six hits in a no-decision.
Both Corbin and Skaggs were selected by the Los Angeles Angels in the 2009 draft.
The pair spent 2009 and 2010 pitching together on the same minor-league teams and were both traded to the Arizona Diamondbacks in 2010. They continued to pitch together in Arizona's minor-league system before they both debuted with the team's big-league club in 2012.
Skaggs was eventually traded back to the Angels in 2013 while Corbin spent six seasons in Arizona before signing an offseason deal with the Nationals this past December.