Having said he “didn’t enjoy” his battling win over Damir Dzumhur in the third round, Alcaraz was far closer to his best on Sunday and had to be against the big-hitting Shelton.
The first set headed to a tie-break after only one unconverted break point for the favourite, but it was Shelton who initially gained the upper hand.
With the crowd roaring their approval as the pair played out a number of stunning points that saw both players at the net, Alcaraz was forced to stave off three set points.
Having done so, the four-time Grand Slam champion took the tie-break but was immediately under pressure in the second set.
Shelton earned six break points in the opening game but was denied each time by Alcaraz, who turned it on late in the set to claim the crucial break.
But Shelton was far from done and after the duo exchanged breaks early in the third set, the 22-year-old from Atlanta saved a break point for a big hold at 4-4.
A helpful net chord gave him two set points in the next game and he took the second to pile the pressure on his Spanish opponent.
Alcaraz quickly regrouped though and broke for a 2-1 lead early in the set. While the pair continued to exchange eye-catching shots, this time Shelton was unable to find a way back.
“Every time we face each other I said we brought the level to the top,” added Alcaraz.
“We entertained the people. He is a really powerful player. He can make any shots.
“I think we played really great tennis. Drops, coming to the net, big shots, and we stayed there the whole match.
“For me, it is great having Ben around, a great energy for tennis and for the people. I love watching him play.”
Later, American 15th seed Frances Tiafoe defeated Germany’s Daniel Altmaier 6-3 6-4 7-6 (7-4).
He will face eighth seed Lorenzo Musetti in the quarter-finals after the Italian beat Denmark’s 10th seed Holger Rune 7-5 3-6 6-3 6-2 in Sunday’s night session.
It is just the second time 2024 Wimbledon semi-finalist Musetti, 23, has progressed beyond the fourth round of a Slam.