A pair of unlikely lob winners had fans gasping in the third game, and he made it 4-0 with a high backhand volley winner that Ruud couldn’t reach.
“My first set, I think I was unplayable to be honest,” Alcaraz said.
“I was really, really happy about playing at that level.”
Meanwhile, defending champion Jack Draper rallied to beat Novak Djokovic 4-6, 6-4, 7-6 (7/5) to reach the quarterfinals.
Draper wore down the 38-year-old Serb superstar in a punishing third set, denying Djokovic his first return to the quarterfinals since the last of his five Indian Wells titles in 2016.
Djkovic, a 24-time Grand Slam champion playing his first tournament since falling to Carlos Alcaraz in the Australian Open final, looked to be feeling the strain as the final set unfolded.
Draper, playing just his second event since missing the better part of six months with an arm injury, kept Djokovic moving with a stream of drop shots.
Ruud stepped it up in the second set, but even he could only smile when Alcaraz seized a 5-1 lead in the tiebreaker with another leaping backhand volley, the Spaniard closing proceedings fittingly with a backhand winner.
“The conditions were difficult, to be honest,” said Alcaraz, who played in chillier night weather in his tough three-set win over Arthur Rinderknech in the third round.
“(It was) really hot, the ball was tough to control. It comes super-fast, it bounces super-high. But I think we played great, both of us.”
Alcaraz, 22, became the youngest man to complete a career Grand Slam with his victory at the Australian Open.
He followed that up with the Qatar Open title and with three wins under his belt in Indian Wells is now 15-0 on the season.
Alcaraz will face 29th-ranked Briton Cameron Norrie for a place in the semi-finals after Norrie beat Australian qualifier Rinki Hijikata 6-4, 6-2.
Norrie won the Indian Wells title in 2021, when the tournament was pushed to October amid the Covid-19 pandemic.