Top seed Mannarino crashes out of Singapore Open
Mannarino, who had beaten Albot in their only previous encounter in Sofia last year, could not repeat that feat again as the Moldovan was clearly at his best.
Despite enduring a gruelling contest where he saved three match points against Germany's Yannick Hanfmann in the second round on Thursday, Albot did not appear fatigued.
"I was ready for today's match. I'm used to playing many matches, so my body is used to that already. I was just trying to fight and I survived," he said.
Albot looked set to win the second set comfortably after cruising to a 5-1 lead before Mannarino staged a comeback.
But Albot fired five aces, with two coming crucially in his last game, to defeat the Frenchman and set up a semi-final clash with Alexander Bublik of Kazakhstan.
"I was very aggressive with my serve today and also feeling confident. I just kept things simple and did all the right things today," said Albot.
Alexei Popyrin knocked out wildcard Matthew Ebden 6-4, 7-6 in the battle of the Australians and will meet former world number three Marin Cilic, who overcame a tense encounter with South Korea's Kwon Soon-woo to win 6-2, 2-6, 7-5.
"It would mean a lot if I can win the tournament this week. I'm missing that confidence and feeling of winning a tournament. Titles do not come that often and you got to appreciate them when they do," said Cilic, who is seeking to end a three-year title drought.