The veteran French showman got his left knee wrapped in the opening set of the first-round match and took confidence from encouraging words from the physio to secure the win which left Britain 0-3 on the day here.
The rush to the exits began with the withdrawal of Andy Murray due to an existing abdominal injury dating to last week in Toronto.
Meanwhile on court, Lorenzo Musetti defeated Dan Evans 6-4, 6-3 before Monfils staged his comeback victory against British number one Norrie.
Monfils has been on a tear in recent days, reaching last week's Toronto quarter-finals as his long return from knee problems gains momentum.
The 36-year-old took down Norrie thanks in part to 41 errors from the world number 15.
"I was quite upset with my knee, but the ATP physio helped me a lot," Monfils said of his taping after the seventh game of the opening set.
"I could push off on it and he told me I could not do any damage; he secured my head."
Monfils broke Norrie twice in each of the last two sets, finishing with a service winner.
"I'm getting better, playing and having fun," the Frenchman said. "I believed more and here I am - I won the match," he said.
Elsewhere Tuesday, Alexander Zverev defeated fellow former tournament champion Grigor Dimitrov 6-2, 6-2.
Germany's Zverev, the 16th seed, claimed the title at his last participation in 2021 while Dimitrov lifted the trophy in 2017.
A year ago, Zverev was healing from ankle surgery following a serious injury at Roland Garros.
The 25-year-old is hoping to turbocharge his hardcourt game after falling in the Toronto second round last week, with the US Open starting on August 28.
Wozniacki bows out
"Last week was really bad for me," Zverev said. "I just played poor tennis. Today I was patient and adjusted a bit better."
Zverev was joined in the second round by former semi-finalist Stan Wawrinka, who polished off a win after rain called a halt to his match the night before.
Switzerland's three-time Grand Slam champion defeated American Brandon Nakashima 6-3, 6-7 (5/7), 6-3, requiring just two concluding games to reach the second round after the overnight pause.
"I hope I can keep pushing it further," said Wawrinka, who now takes on another American in 10th seed Frances Tiafoe.
Borna Coric concluded unfinished business with Petra Korda, winning 7-6 (7/5), 6-4 while Ugo Humbert defeated fellow Frenchman Arthur Fils 6-4, 3-6, 6-2.
In the WTA draw, the continuing career comeback of former number one Caroline Wozniacki failed to ignite as the Dane went down to French lucky loser Varvara Gracheva 6-4, 6-4 in 96 minutes.
Wozniacki, 33, won her first comeback match a week ago in Montreal before losing in the second round to Wimbledon winner Marketa Vondrousova.
"I didn't play very well and never found my rhythm," Wozniacki said after Tuesday's loss.
"I tried to fight but it was one break in each set. I just didn't return well enough either... I had nine breakpoints and won none of them.
"That's just not good enough when you're playing against players on this level; we'll have to work on that."
Three-time Grand Slam runner-up Ons Jabeur, playing for the first time since losing last month's Wimbledon final, survived a struggle with Anhelina Kalinina of Ukraine to reach the third round 6-3, 6-7 (2/7), 7-6 (7/2).
All England Club title winner Marketa Vondrousova beat Katerina Siniakova 7-5, 6-4.
Two-time Cincinnati winner Victoria Azarenka rallied from 1-4 down in the second set to overhaul Barbora Krejcikova 6-3, 7-5.
Azarenka's fellow double Grand Slam champion Petra Kvitova took down Anna Blinkova 7-6 (7/2), 6-0.
