However on the following point, Djokovic hit a powerful inside out down the line forehand which Alcaraz netted in a crosscourt forehand to reach 6-6.
Alcaraz netted two additional forehands as well as a backhand to drop the set before receiving treatment during a medical time for a right finger injury.
In the final set, Djokvic broke serve to lead 4-3 before holding serve to lead 5-3.
Alcaraz held serve then broke serve to level the match at five games all.
Both players won their following service games to reach a tiebreaker.
Djokovic took a 3-0 lead after Alcaraz struck two forehands long.
Alcaraz rebounded to level the tiebreaker at three points all after striking a down the line forehand volley winner.
However he then hit several crosscourt forehand errors to drop the tiebreaker and the match.
Alcaraz finished the match with 42 winners to 50 unforced errors to 19 winners and 46 unforced errors for Djokovic.
In a surprise tactic, Djokovic won 20 of 28 net points and finished the match with 133 overall points to 128 points for Alcaraz.
Djokovic won grand slam titles at this year's first two grand slams: the Australian Open and Roland Garros.
Alcaraz won his first grand slam title at last year's US Open in September before defeating Djokovic in the final of Wimbledon in July.
Djokovic will most likely regain tennis' top ranking after the US Open as he is not defending any ranking points in New York while Alcaraz as the defending champion is defending 2,000 rankings points.
The US Open is scheduled to be played in New York August 28th - September 10th.