gained revenge on to reach the Italian Open semi-finals and guarantee he will be the No.2 seed at the French Open.
The British No.1 had beaten the reigning French and Wimbledon champion in their last meeting in the Indian Wells semi-final in March.
But in their first ever meeting on clay, the Spaniard won a fascinating match 6-4 6-4 to show he will be the man to beat in Paris.
Draper had chances to win a tight second set. But the defeat also dampens expectation for world No.5 Draper's chances at the claycourt Grand Slam which starts on May 25. He reached the final of the Madrid Masters but has still to win a claycourt event.
Alcaraz won all four of his break points while Draper could convert only two out of eight and hit only eight winners.
The two superstars, who share great mutual respect, embraced warmly at the net, at the end of the contest.
Draper had made the first break of the match to lead 4-2 in the first set when the Spaniard served a double fault on the second break point.
But Alcaraz responded by winning the next five games. He immediately broke Draper to love - and broke again to serve for the set at 5-4. The Spaniard took his first sset point after 43 minutes when the British No.1 hooked a backhand into the tramlines.
The Wimbledon champion seemed set for a quick win when he took his third break point out of three to win the first game of the second set with backhand volley winner.
But Draper responded by breaking back to 1-1 and Alcaraz had to save two big break points in the arduous eighth game before drawing the set level at 4-4.
Invigorated by the hold, Alcaraz then broke to love and took his first match point after a Draper forehand error after one hour and 37 minutes.
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