Evans, a 33-year-old from Britain, saved four break points in the last game before ending the match with a service winner. He is the oldest champion in Washington since Jimmy Connors was 35 when he won the event in 1988.
Evans arrived in Washington with an 8-18 record this season before going 5-0.
“I had to keep telling myself it was match-by-match and not so long ago I wasn’t playing great,” he said. “It was a good effort mentally to just stay in the present and keep fighting for each point. And I did a great job of that this week.”