The fourth-ranked Australian Open runner-up Murray mauled German Michael Berrer 6-4, 6-2 in 71 minutes, while the world No. 9 Monfils smacked 11 aces and held off Colombian Santiago Giraldo 6-4, 4-6, 6-1 on the hardcourts at Impact Arena.
"I served well throughout," said Murray, who arrived in Bangkok on Monday afternoon. "I'm still trying to overcome the jetlag a little bit, as I find it difficult traveling East. I started playing better in the second set, moving well."
Up next for the Scottish Murray will be promising Bulgarian Grigor Dimitrov, while the French Monfils' quarterfinal opponent on Friday will be last year's Bangkok runner-up Jarkko Nieminen. The Finnish veteran Nieminen lost to Spaniard Guillermo Garcia-Lopez in last year's Bangkok finale.
The tournament lost its reigning champion on Day 4 when American Donald Young ousted a fourth-seeded Garcia-Lopez 6-1, 6-7 (0-7), 7-5. Young prevailed in 2 hours, 38 minutes with the help of five service breaks.
Other second-round action saw Dimitrov douse Italian Simone Bolelli 7-6 (10-8), 6-1 and Japanese qualifier Go Soeda best German Tobias Kamke 6-2, 7-6 (9-7). Soeda will battle Young on Friday.
Another quarterfinal on Day 5 will pit third-seeded Frenchman Gilles Simon against upstart German Matthias Bachinger. Simon titled here two years ago.
The 2011 Bangkok titlist will earn $107,000.