World number one and Australian Open winner Sinner raced past 87th-ranked Christopher O'Connell of Australia 6-1, 6-4, 6-2.
The 23-year-old Italian's win came a day after four-time champion Djokovic was sent spinning to his earliest loss in New York in 18 years by Alexei Popyrin.
One day earlier, 2022 winner Alcaraz was defeated in the second round by Dutch journeyman Botic van de Zandschulp.
"Today was great match. I knew I had to play very solid. My serve worked well so I am happy with my performance," said Sinner after firing 15 aces in his 46 winners past the outclassed O'Connell.
Sinner did not face a single break point in his one-hour 53-minute victory which took him into the last 16 for a fourth successive year.
"There have been some upsets in the tournament so let's see what's coming. I'm happy to still be here and play as many matches as possible," added Sinner whose comfortable afternoon on Arthur Ashe Stadium saw tennis legend Serena Williams amongst the spectators.
With Djokovic and Alcaraz heading home to Europe, Medvedev finds himself as the only former champion left in the men's tournament.
The eccentric Russian, seeded four, faces Flavio Cobolli, the world number 31, one of three Italians in third round action.
Medvedev famously shattered Djokovic's bid for a rare calendar Grand Slam when he captured the 2021 title in New York.
This year he was runner-up to Sinner at the Australian Open and made the semis-finals of Wimbledon but is without a tour title since winning the Rome Masters in May last year.
Britain's Jack Draper made the last 16 for a second successive year by defeating Alcaraz's conqueror Botic van de Zandschlup 6-3, 6-4, 6-2.
Women's world number one and 2022 champion Iga Swiatek dropped one game and secured a season-leading 55th win of 2024 by routing Ena Shibahara on Thursday.
On Saturday, she takes on 33-year-old Anastasia Pavlyunchenkova, who will have revenge on her mind after suffering a 6-0, 6-0 blowout when she met Swiatek on the Rome clay last year.
'I'm a fan'
Pavlyunchenkova is a vastly experienced Grand Slam campaigner, making the 2019 French Open final as well as seven other quarter-final appearances.
One of those came at the US Open in 2011 where she was stopped by Serena Williams.
Meanwhile, 2023 semi-finalist Karolina Muchova, who knocked out two-time champion Naomi Osaka in the second round, cruised into the last 16 by beating Anastasia Potapova 6-4, 6-2.
She next faces French Open and Wimbledon runner-up Jasmine Paolini, the fifth-seeded Italian, who beat Yulia Putintseva 6-3, 6-4.
Paolini has now made the fourth round of all four Slams this year having previously never got beyond the second round in 16 attempts.
"I'm a fan of her (Muchova). I really love how she plays. She can play every shot, slice, volleys, serve and volleys. She's a very complete player," said Paolini.
US sixth seed Jessica Pegula made the last 16 for a third successive season by defeating Jessica Bouzas Maneiro 6-3, 6-3.
Pegula, one of three American women to have made it so far to the second week, next faces Diana Shnaider.
The 18th-seeded Russian made the fourth round of a Slam for the first time by seeing off 37-year-old Sara Errani in straight sets.
Czech Republic's Tomas Machac, ranked 39, also reached the fourth round of a major for the first time by defeating Belgian veteran David Goffin 6-3, 6-1, 6-2.
He will take on Draper for a spot in the quarter-finals.
