Then with Tsitsipas serving down 3-4, Alcaraz struck a crosscourt inside out forehand dropshot winner to reach breakpoint.
The Greek netted a down the line forehand passing shot to lose serve and trail 3-5.
Another forehand error from Tsitsipas in the following game ended the set as Tsitsipas netted a down the line forehand passing shot when facing set point.
In set two Alcaraz continued to execute powerful groundstrokes to score a break of serve before serving for the match at 5-4.
Alcaraz struck an overhead winner which he followed up with an inside out crosscourt forehand dropshot winner to lead 30-0.
The Spanaird then struck a down the line forehand passing shot winner to lead 40-0 and reach match point.
Alcaraz hit an inside out down the line forehand winner to take the match after one hour and 18 minutes of play.
If you subtract the rankings points from this week's tournament in Madrid as well as next week's tournament in Rome, Alcaraz would trail
the world number one Novak Djokovic of Serbia by only five points at 5,770 to Djokovic's 5,775.
Alcaraz can reclaim the number one ranking following Madrid and Rome in four different scenarios.
If Alcaraz wins Madrid and plays his first match in Rome, we will reclaim the number one ranking.
Or if Alcaraz wins Rome after playing a match in Madrid, he would return to the top ranking after Rome.
If Alcaraz reaches the final of both Madrid and Rome, he can reclaim the number one ranking.
Alcaraz needs to win enough matches between the two tournaments of Madrid and Rome for a combination of more than 1,005 points to regain the top ranking.
Following his stunning US Open title win in September, the 19 year old Alcaraz became the youngest ever men's
number one and the only male teenager to ever reach number one.