The four-time Grand Slam champion finally pulled through 6-7, 6-4, 7-6 in the longest men's singles match in the tournament's history.
The Spaniard, who will return to number two in the world behind Sinner, was 3-0 down in the final-set tiebreak only to fight back and win in three hours and 21 minutes.
The 21-year-old said the victory was all the more satisfying following a disappointing second-round exit at the US Open, where Sinner went on to triumph.
Alcaraz also went out in the round of 32 at the Cincinnati Masters in August.
"Probably after the American swing, I was a little bit down," he said in Beijing, his trophy sitting in front of him.
"I didn't want to touch a racquet for a while. I didn't want to travel."
He credited his coaching team with helping to drag him back to his old self.
"After that we talked a lot during those days, knowing that I have to be back practising, be stronger physically, be stronger mentally just to overcome problems.
"The last month we've been working really, really hard on the court, off the court, just to be able to feel this moment again."
His coach Juan Carlos Ferrero was in tears at the end and Alcaraz said it showed what it meant to him and his team.
"Thanks to them I started to get the joy back playing the matches, practising, I got motivated again," said Alcaraz.
"I really wanted to travel, to play tournaments again."
