It was a 6-3, 6-3 win as he made it seven matches in a row unbeaten on home soil. This began with his Atlanta title run last week.
Next up is Tallon Griekspoor on Saturday for a spot in the final. The Dutchman defeated both Gael Monfils and J.J Wolf also on Friday.
"I've put in a lot of work the last couple of weeks before coming here. I knew that this is one of the most physically demanding parts of the season, playing in the heat," Fritz said post-match.
"I definitely wasn't training and preparing to play two matches in a day, especially one following a three-hour match.
"I came out tonight in the second match playing really well, being aggressive. I got early breaks in both sets, which was kind of my strategy, to kind of give it everything I had early, get up a break, and then I could coast a bit and focus on my serve games."
In the bottom half of the DC draw, Grigor Dimitrov advanced through walk-over against Ugo Humbert. He pulled out with a left leg injury.
The fifth seed will now face Dan Evans who took down Alexander Shevchenko followed by Frances Tiafoe.
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5.39pm: Fritz defeats Murray after 3 hours 2 minutes
8.30pm: Fritz walks onto court to face Thompson
9.59pm: Fritz defeats Thompson to make the semis, totalling 4 hours 20 minutes of play
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