Sinner reaches first French Open semi-final, to become world No.1
The Australian Open champion, who will move top of the rankings next week after Novak Djokovic's withdrawal from the tournament, eased to a 6-2, 6-4, 7-6 (7/3) victory and will take on either Alcaraz or Stefanos Tsitsipas in the last four.
Sinner's achievement of becoming Italy's first number one in the sport was confirmed during his match, as the injury-enforced withdrawal of Djokovic was announced.
"What can I say?" said the 22-year-old.
"It's every player's dream to become number one in the world. On the other hand, seeing Novak retiring (from the tournament) is disappointing, so I wish him a speedy recovery."
Sinner already knew that he could take the number-one berth by reaching the final at Roland Garros.
He has enjoyed a fine season, also winning the Rotterdam and Miami Opens in addition to his maiden Grand Slam title in Melbourne.
"I'm trying not to think about it too much as this has been a tournament I've struggled in the last couple of years so I'm very happy to be in the semi-finals," Sinner added.
"It's a special moment for me... for people watching in Italy. Let's see on Friday what I can do."
Sinner's win-loss record this year now stands at an impressive 33-2, his only two defeats this season coming against Alcaraz in the Indian Wells semi-finals and Tsitsipas in the Monte Carlo last four.
If Sinner is to reach a second successive major final, he will have to overcome Alcaraz, against whom he shares a 4-4 head-to-head record, or Tsitsipas, who he has lost to six times in nine meetings.
Alcaraz faces former Roland Garros runner-up Tsitsipas in Tuesday's night session.
Sinner dominates
Bulgarian 10th seed Dimitrov was playing in the quarter-finals for the first time on his 14th French Open appearance, and was largely outplayed despite a brief late rally.
Sinner eased to the opening set, breaking twice and losing just four points behind his serve.
He broke again in the first game of the second set and comfortably held from then on to move closer to the semis.
It was a similar story for much of the third, as Sinner set up the chance to serve for the match when leading 5-4, but Dimitrov finally put him under pressure to level the set.
The second seed gathered himself, though, to force a tie-break, which he dominated to add another career first on an already landmark day for himself and Italian tennis.
"My performance was solid, a little bit of tension when I was serving for the match which is normal, but I'm very happy to be in the semi-finals," he said.