By Matt Majendie
Monfils, the number 17 seed, praised Gasquet as the stronger player before the pair stepped on court but then had little trouble during the two-hour, 35-minute affair.
Gasquet had a chance to serve for the second set but his form dramatically eluded him and, with it, his chance to advance at the year's final grand slam.
Monfils was all smiles with his close friend after the match - the pair exchanged kisses on either cheek on court - but he laid into his rival afterward.
"With the first set point he had in second set, he could have passed me easy but he showed me at that time he was not that good mentally," said Monfils. "He showed me he was, I won't say weak, but it was like a bit shaky.
"Richard doesn't really like pressure like that... so I just played with that, played a bit with his mind and that was it."
Monfils was the fan favorite from the moment he stepped on court at Louis Armstrong Stadium and, when the noise of the crowd dropped slightly, he whipped them into a frenzy.
"The crowd helped me for sure in the second set. After I served the set point, I asked the crowd to get involved a bit, and they did," he said. "That's why I broke him straightaway, because I had positive energy.
"I love when it's intense, I love it. It makes me feel like I'm stronger again, so for sure when the crowd gets involved I play my best tennis."
Whatever happens in the next round, Monfils has already achieved his best result in five U.S. Open appearances. He now faces Novak Djokovic for a place in the last four after the number three seed's straight-sets demolition of Mardy Fish.
"I have revenge to take because he won against me at home in Bercy," said Monfils, referring to his loss to Djokovic in the Paris Masters final last November.
"So, this time I hope to win."