That sets up a semifinal against No. 7 seed Alex de Minaur of Australia, who toppled No. 4 seed Borna Coric of Croatia 6-2, 4-6, 6-4.
Mannarino, who now meets his Australian practice partner Alex de Minaur, started with a flourish as he reeled off the opening seven games to stamp his authority on the match.
The pair may not have to wait for long to play each other again, as first-round wins at next week's Japan Open would set up a last-16 showdown.
"Conditions are really humid here and it was really physical, but I was able to stay really concentrated", the 31-year-old Mannarino said.
"I think it's knowing exactly what the other person is going to do at a certain time in the match, trusting each other 100 per cent and knowing that each one of us is willing to work hard 100 per cent every day to get better", said Vliegen.
De Minaur failed to win a break point until the final point of the match, but never faced a break point of his own.
He powered past three-times Grand Slam victor Andy Murray, World No 14 Borna Coric and 10th-ranked Roberto Bautista Agut en route to Sunday's championship match.
"If I can try to bring this level nearly every week, then I'll be going deep in tournaments and beating these top guys and pushing for titles".