Shelton next faces Carlos Alcaraz and the 23-year-old showed he has the tools to trouble the Spaniard, though he said that it would take special tennis to beat the defending champion who has hit top form after an injury lay-off.
"The level that he's playing at is really impressive. To not play for almost five months and do what he's doing is superhuman and we're happy to have him back," Shelton said.
"He lights up stadiums and I think there's going to be fireworks again on Tuesday."
Shelton blended raw power with a delicate touch and sharp decision-making to overwhelm Tsitsipas on Arthur Ashe Stadium.
"My team told me that if I didn't show up fully focused they would leave," joked Shelton, who is bidding to become the first US man to win a major since Andy Roddick's 2003 triumph at Flushing Meadows.
"I was focused, it was a good match from start to finish. It was my first straightforward match this year and I'm happy I can play this way in front of you."
Earlier on Sunday (Monday AEST), Alcaraz beat American 20th seed Tommy Paul 6-4 6-3 6-4 in a high-voltage hit-fest to remain firmly on track for back-to-back titles in New York.
The seven-time grand slam champion has extended his major match-winning streak to 18 with a stunning display against a fellow big-hitter.
Alcaraz's serve came under pressure in the third game when Paul fired an exquisite 160km/h forehand winner around the net that brought Arthur Ashe Stadium to its feet, but the 23-year-old Spaniard stood firm before striking late to snatch the opening set.
Even with much of the showcourt crowd yearning for a home winner, second seed Alcaraz continued to steal the show with his audacious play and improved his win-loss record against American players at the grand slams to 13-0.
"I played my game. I tried to play my style," Alcaraz said in the on-court interview after his win.
"Tommy is such a talented player. His shots are pretty dangerous and sometimes it is really difficult to control the ball when it comes to you.
"... I'm really happy with the performance today."
American Frances Tiafoe outclassed former champion Daniil Medvedev 7-6 (7-1) 6-4 7-6 (8-6) to to book his spot in the last eight.
Tiafoe trailed Medvedev 1-6 in career head-to-head, with his only victory coming at the team competition Laver Cup, but he cracked the code when it mattered to him the most, repeatedly striking near the net with surgical precision.
"Daniil has been so good, he's beaten me so many times. This is the first time I've beaten him in a regular match," said the 11th seed.
"Everything is feeling really good. I'm coming forward, I'm having fun."
Tiafoe will next play compatriot Alex Michelsen.
