Three-time Grand Slam winner Murray was a finalist in the Washington event in 2006Andy Murray won his first singles match since Wimbledon when he defeated American Brandon Nakashima in straight sets at the Citi Open in Washington.
The British player will now face the winner of Taylor Fritz's match against Zachary Svajda in the last 16.
"I thought I did well, I hit the ball well from the beginning," he said.
"I was struggling a little bit on the return. Brandon serves well, especially his second serve.
"I was struggling to create many opportunities on return. But I was just a little bit more solid than him at the end of the tie-break. He made a few mistakes, I put enough balls back in play.
"The courts and the balls are extremely slow here, so you're having to work really hard in all of the games, it's not easy to finish points. It was a good one to get through," the Scotsman added.
British number two Dan Evans also won, coming from a set down to beat France's Gregoire Barrere 2-6 6-0 6-3, but Liam Brady lost against the Netherlands' Tallon Griekspoor 4-6 2-6.
Evans, 33, will face Russia's Alexander Shevchenko in the next round.
Elsewhere, Wimbledon surprise package Chris Eubanks beat Japan's Sho Shimabukuro 6-3 6-4.
American Eubanks, 27, who reached the quarter-finals in his first appearance at the Grand Slam before losing against Daniil Medvedev, will take on Australian Jordan Thompson in the last 16.
