The 22-year-old Shelton went toe-to-toe with the Frenchman, 16 years his senior, until Monfils pulled the plug exhausted in the fourth set.
Shelton won 7-6(7/3), 6-7(3/7), 7-6(7/2), 1-0 with each of the first three sets lasting almost an hour.
“At 38 years old I hope I’m still walking without crutches,” Shelton, who matched his 2023 run to the last eight at Melbourne Park, said of Monfils.
“To push me the way he did the way he did today and entertain everyone is so impressive.”
Monfils, ranked 41, upset fourth seed Taylor Fritz in the third round, but the exertion of several long matches on the back of winning the lead-up Auckland Classic took its toll.
“He had played a lot of long matches and I wanted to make it as physical as possible,” said the 20th-ranked Shelton, whose best Slam result came in 2023 when he made the US Open semifinals.
“It was really tricky today because he was serving so well. There’s a lot of things that make that guy a nightmare to play.”
There was nothing between them in the first set which went to a tiebreak where Shelton won the last four points to get over the line.
Another close battle unfolded in set two which again went to a tiebreak when neither man could force a decisive break.
This time it was the Frenchman that came out on top, unleashing a forehand winner to level the match.
They exchanged the first breaks of the contest early in Set 3.
But again nothing separated them until Shelton ended the resistance of Monfils with a series of winners to take the tiebreak and the veteran retired soon after.
Shelton will next meet Sonego, who blasted into his first Grand Slam quarterfinal on his 26th attempt.
The seasoned 29-year-old proved a bridge too far for 19-year-old American Tien, who stunned fifth seed Daniil Medvedev in Round 2.
Against the world No 55, Tien wilted, succumbing 6-3, 6-2, 3-6, 6-2 with a right thigh problem not helping.
It brought the curtain down on a breakthrough debut tournament for Tien, who was bidding to become the youngest man to reach the quarterfinals since Goran Ivanisevic in 1989.
“Unbelievable. It’s pretty emotional, today was tough,” said Sonego.
“So sad because he had some problem. It’s not the right way to win but I’m so happy to reach the quarterfinals.
Tien was broken to love on his first service game with the Italian giving him little opportunity to strike back.
Sonego was untouchable on his first serve, winning 100% in Set 2, to again limit Tien’s chances.
The American slumped 5-2 behind before leaving the court for a medical timeout after treatment on his thigh.
When he returned, Sonego wrapped up the set with ease, but against the odds Tien recovered with a dominant break to start Set 3, holding on to give himself a glimmer of hope.
But he was spent as Sonego took charge again in the fourth set.