The world No. 4 Australian Open runner-up Murray handled rising Bulgarian Grigor Dimitrov 6-4, 6-4, while the flashy Frenchman Monfils topped last year's Bangkok runner-up Jarkko Nieminen 7-5, 7-6 (7-4) on the hardcourts at Impact Arena.
The Finnish Nieminen lost to Spaniard Guillermo Garcia-Lopez in last year's Bangkok finale.
The Scottish Murray, the 2005 Bangkok runner-up, will tangle with 2009 titlist Gilles Simon in Saturday's semifinals. The third-seeded French Simon charged back to beat German Matthias Bachinger 3-6, 6-3, 6-2 on Friday.
Murray is 7-1 lifetime against the former top-10 Simon, who has dropped seven straight in the series, including three setbacks already this season.
Meanwhile, surging American Donald Young reached his second semifinal of the year with a 6-1, 6-2 shellacking of Japanese qualifier Go Soeda on Day 5. Young ousted the reigning Bangkok champion Garcia-Lopez on Thursday.
"I hope to go further. Every time you make it into a stage, the second time you hope to go further," Young said. "When you win a tournament you want to repeat."
Young should have his hands full with Monfils on Saturday.
"He gets a lot of balls back," Young said. "He's in the top 10. He beat me pretty bad the last we played." Monfils pasted Young 6-1, 6-1 in Cincinnati back in 2008.
The 22-year-old Chicago native Young, who reached the fourth round at the U.S. Open earlier this month, is projected to land inside the ATP's top 50 for the first time in his career on Monday.
The 2011 Bangkok titlist will earn $107,000.