World number 31 Mannarino rallied in the second and broke Goffin to take a 4-2 lead but the in-form Belgian responded by breaking the Frenchman immediately and once more in the 11th game as he charged to victory.
London finals hopefuls Marin Cilic and David Goffin have strengthened their year-end chances, with the pair reaching the Japan Open semi-finals through resounding straight-set wins.
"The quality of the game was really good but I wasn't good enough compared to him", he said.
Gasquet broke Lu's next service game before the Taiwanese player broke back to level at 3-3.
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Gasquet had three set points on serve at 40-0 in the ninth game, but the Belgian won that and the next six games.
"I wouldn't say that I am disappointed, I played quite solid", Cilic said. The No. 2 seed then held on to his serve to close out the first set. "My second serve is really effective; my opponents don't attack me, so I'm ready to play the second shot". "In the last set and a half he didn't miss much".
Johnson now faces eighth seed Diego Schwartzman in the quarter-final after the Argentine disposed of Australia's Bernard Tomic. However, he committed three straight forehand errors to give Goffin the opener.
Although he took time to work his way into the match, incredibly he held one set point at 5-4, Advantage, in the second set when Schwartzman was serving. But Schwartzman stormed back and eventually forced another tiebreak.
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Goffin came from a 5-2 deficit in the opening set and completed his recovery by sweeping 10 of 11 games in a match lasting just over 90 minutes.
"When you've won a lot of matches you know how to play the important moment - you have a great feeling on court, confidence", Goffin said.
"I don't know if he served worse or I returned better but it changed a lot from the middle of the second set - then I was risky in every service game of Marin's", Mannarino said.
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By contrast, Red Bull Racing disappointed, with Daniel Ricciardo finishing fourth, one place ahead of Max Verstappen . Kimi Raikkonen was sixth but, like Bottas, will also drop five places on the grid after requiring a new gearbox.