In promising signs ahead of next month's US Open, the Australian No.1 and seventh seed stormed to a 6-4 6-3 victory at the event where he reached his maiden ATP 500 final back in 2018.
While not perfect on serve, broken twice, de Minaur broke the world No.59 five times from his 10 service games in the victory, which took one hour and 45 minutes.
However, the 26-year-old world No.13 will need to lift his game in the final, after committing 33 unforced errors against the Frenchman, including 21 in the first set, and 21 on his backhand for the match.
"It wasn't pretty tennis, but I knew it was going to be a tricky match without a lot of rhythm,'' de Minaur said.
"That's what he's able to do to opponents. I had the mentality of doing whatever it took to get into the title match tomorrow.''
One part of his game that worked well in the semi was at the net, where he won 17 of 22 points as he regularly attacked Moutet's weaker backhand wing.
De Minaur, who would love to go one step further in Washington after losing in straight sets to Germany's Alexander Zverev in the 2018 final, improved to a tour-leading 21 hard-court wins for the season.
The Aussie also has 41 wins at ATP 500 level since the start of the 2023 season, which is the most by any player.
De Minaur will return to the top 10 in the rankings after reaching the final, where he will face 12th seed Alejandro Davidovich Fokina.
The Spaniard followed up his quarter-final win over top seed Taylor Fritz by beating another American, fourth seed Ben Shelton, in straight sets, 6-2 7-5.Â
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