Sinner, who won 6-7(5), 6-3, 6-3 to bag the $6 million title, said he hoped for a long rivalry with Alcaraz, after Rafael Nadal and Novak Djokovic faced off for the final time in the third-place match earlier in the day.
"I wake up in the morning trying to understand the ways how to beat him. This kind of rivalries, this kind of players, they push us always to our 100%," world number one Sinner said in a post-match interview.
"Hopefully this rivalry will last as long as possible. But there are so many other great players who can jump in ... let's see what's coming in the future," he explained.
Italy's Sinner and Spain's Alcaraz have won two Grand Slams each this year, with Alcaraz beating Sinner in closely fought clashes at the French Open semi-finals and the China Open final.
The off-the-court friends have played each other 10 times on the ATP tour, with Alcaraz winning six matches, including the last three.
"I will do everything so that this rivalry gets better and better ... I am happy to share the court with him," four-times Grand Slam winner Alcaraz said.
