Frenchman Monfils fired down 10 aces and deployed the kind of creative shotmaking that has endeared himself to tennis fans in the California desert for years, soaking in the applause on a sunny centre court after sealing the dominant win.
His compatriot Arthur Fils, who advanced with a straight sets win over Nuno Borges, said Monfils was an inspiration.
"I don't know how he did that because we were talking before the match about how Purcell is a very good opponent," Fils told reporters.
"Then I went to take a nap and woke up and it was 6-1, 5-2? I think everyone on the tour wants to see him play more and more years.
"It would be very nice to play with him in doubles one day."
Monfils will battle eighth seed Hubert Hurkacz of Poland in the second round while Fils faces Spaniard Alejandro Davidovich Fokina, who is seeded 23rd.
Earlier, Wawrinka fell 7-6(3), 4-6, 6-2 to Machac as the Swiss continued his poor recent form.
Wawrinka, who reached a career high of world number three a decade ago, was unable to match the Czech's level in the deciding set, his signature one-handed backhand sailing wide on match point.
Wawrinka lost in the first round of this year's Australian Open, the second round of the Argentina Open, and the Rio Open first round before coming to the California desert, where he was a finalist in 2017.
Machac will play French 21st seed Adrian Mannarino in the second round on Saturday.
Croatian Borna Coric, Russian Roman Safiullin, China's Shang Juncheng and American teenager Alex Michelsen were among other players who advanced to the second round on Thursday before play was halted for the second consecutive day due to rain.
