Rublev upset home favourite Alcaraz 4-6, 6-3, 6-2 to reach the semi-finals.
The seventh-seeded Rublev had lost his last five matches against top-three opposition and was 0-1 head-to-head against Alcaraz coming into the contest.
He was also on a four-match losing streak heading into the Madrid Open.
All that seemed like a distant memory in the quarter-finals against Alcaraz as Rublev maximised on his powerful brand of tennis to shock the Spanish world number three and reach the semi-finals at a seventh different Masters 1000 tournament, from a full set of nine.
Alcaraz missed the clay-court tournaments in Monte Carlo and Barcelona last month due to a forearm injury and needed a third-set tiebreak to squeeze past last year's finalist Jan-Lennard Struff in the fourth round on Tuesday.
He couldn't hold off an inspired Rublev though, his quest to become the first man to win three consecutive titles in Madrid coming to a crashing halt.
"I think the key was that I think it was one of my first matches that I was completely calm all the match, I didn't say one word, even if I was losing," said Rublev, who now owns at least one victory against each of the current world's top 10.
Alcaraz played a convincing first set, breaking serve in the fifth game en route to a 41-minute lead. But Rublev brought his A-game to take the next two sets and finished the match in just under two hours, firing 30 winners along the way.
He awaits Taylor Fritz or Francisco Cerundolo in the final four.
Alcaraz says it has been a positive week in Madrid overall but admits he is still thinking about his forearm, whether it is painful or not.
'Close to 100%'
"Today probably I felt more in the forearm than yesterday's match. Playing three hours yesterday, I knew that I'm going to feel something or I'm going to think about it even more."
The two-time Grand Slam champion acknowledged he has to be patient with regards to his recovery, adding: "I'm going to go to Rome. I'm going to work these days to be close to 100 percent or in a good way to play Rome, but I'm going to decide these days."
Sinner was due to face Felix Auger-Aliassime in the quarter-finals on Thursday but revealed he has been battling through a hip issue this week in the Spanish capital.
"My hip has been bothering me this week and has slowly been getting more painful. Taking the advice from the doctors we decided it's best to not play further and make it worse," wrote Sinner in a statement on social media.
The Italian has won 28 of 30 matches played so far this season, which has yielded him three titles at the Australian Open, Rotterdam and Miami.
Sinner is due to play on home ground at the Italian Open in Rome next week before heading for an assault on the French Open, the season's second major, which starts in Paris on May 26.
Earlier, Elena Rybakina battled back from 2-5 down in the deciding set and saved two match points to overcome Yulia Putintseva 4-6, 7-6 (7/4), 7-5 and reach the semi-finals of the WTA event.
Fourth seed Rybakina produced key serves to swat away two match points at 2-5 and broke Putintseva as she was serving for the victory at 5-3.
In the first all-Kazakh quarter-final at this level on the women's tour, Rybakina lacked efficiency on her break point opportunities, converting just three of 12 chances, and struggled to deal with Putintsev's deft drop shots.
But a late-match collapse from Putintseva, who smashed her racquet and left it on court after the match, helped Rybakina advance to her sixth semi-final of the season, where she will face defending champion Aryna Sabalenka or 17-year-old Mirra Andreeva.
Rybakina owns a tour-leading 30 wins in 2024, and has been successful in her last 12 deciding sets this season.
