The bench coach managed the final eight-plus innings of NLDS Game 2 after Williams was tossed in the 10th inning.
The bench coach spent four days in Arizona with Williams so the two could get to know each other better.
Randy Knorr, the players' choice to succeed Davey Johnson, will remain on board and serve as Matt Williams's bench coach.
Randy Knorr, considered the top in-house candidate to replace Davey Johnson, interviewed with the Nationals late last week.
The Nationals' bench coach was angry on Thursday after Ian Desmond was plunked and the umpire warned the benches.
The Nationals manager deferred to Knorr and his decision-making.
Randy Knorr doesn't let Rafael Soriano finish the ninth inning: "If you don’t want to be in that mode to shut the game down, I’ll bring somebody else in."
In an interview earlier this week with a Canadian radio station, bench coach Randy Knorr said he asked Davey Johnson in the moment if he wanted to walk Pete Kozma.