It appeared the best match-up of the fourth round in the bottom half of the draw, but seventh seed Dimitrov was off his game and went down 7-5 7-6 (8/6) 7-5.
Monfils, who is likely to meet Roger Federer next, is one of the most enigmatic characters on tour and infuriates as much as he entertains with his frequent inability to turn talent into results.
But for most of yesterday’s match, which was played in high humidity, he was calm and controlled, allowing Dimitrov to implode under the weight of expectation.
The Bulgarian cracked first in the 11th game of the opening set, with Monfils serving it out confidently.
The Frenchman saw an early break slip away in the second and had a brief meltdown but it was Dimitrov who collapsed in the tie-break, four errors from 6-4 handing the set to Monfils.
When he served to stay in the match in the 12th game of the third, Dimitrov again faltered, finishing the contest with a meek double fault.
Monfils’s only previous trip to the last eight at Flushing Meadows came four years ago, when he lost to Novak Djokovic.
The Frenchman, who is yet to drop a set, also made the quarter-finals at the French Open this year, going down in five sets to Andy Murray.
Peng Shuai raced into her first grand slam semi-final with a convincing win over 17-year-old Belinda Bencic.
Swiss teenager Bencic has attracted most of the attention for her run to the last eight, which included the first two victories over top-10 players of her career.
But she was totally outplayed by Peng, who is yet to drop a set in the tournament and blasted 24 winners in a 6-2 6-1 victory. The 28-year-old becomes the third Chinese player after two-time grand slam champion Li Na and Zheng Jie to reach the last four at a grand slam.
The breakthrough has come in her 37th slam tournament, and Peng said: “It’s an amazing time for me. It’s a little bit too exciting.
Peng showed in the second round by beating Agnieszka Radwanska that she was in great form and she was always in control against Bencic.
The Chinese player, ranked 39th, was simply too consistently good, and it was not long before the teenager was showing her frustration.
Bencic received a warning for coaching by her father Ivan early in the second set and only just avoided a love set.
It has nevertheless been a superb tournament for Bencic, who has worked with Martina Hingis’s mother since she was four.
Ranked 331 a year ago, she is the youngest player in the top 100 and is projected to climb into the top 35 next week.
Serena and Venus Williams lost in the quarter-finals of the women’s doubles 7-6 (7/5) 6-4 to fourth-seeded Russian pair Ekaterina Makarova and Elena Vesnina.