Harry Viljoen's team won 43-20 after battling to a 22-15 lead at halftime.
This June's Test will be the 34th between the Boks and Wales, with the South Africans having won 28 and lost four, while one encounter ended in a draw.
SA Rugby chief executive Jurie Roux said the Boks were delighted to play against Wales on US soil.
"The match allows us to take rugby to America, and to potentially expand the team's appeal to a very large audience."
The stadium in Washington is located near the well-known US Capitol building, and has a seating capacity of 45 000.
The match will allow the new national coaching team to see the 2018 Boks in action before the visit by Eddie Jones and the England team a week later.
The three-Test series starts at Ellis Park on June 9, with the second and third Tests scheduled for Bloemfontein and Cape Town.
There was not confirmation of the previously reported claim that if the test in Washington went ahead, the Springboks would draw on South Africans playing in Europe to save most of their South African players from the stress of travelling for the England test the following week.
Erasmus, who was named SA Rugby's director of rugby a few weeks ago, is expected to be unveiled as the Boks' new head coach in the coming days, taking over from the now-departed Allister Coetzee.
Under Coetzee, who was in charge during 2016 and 2017, they slipped down the rankings and are now in sixth place.
Wales are in seventh spot, but Warren Gatland's side have won the last two meetings between the teams, both in Cardiff.
