
The result in the round-robin grouping means that Djokovic, beaten in his opening match on Sunday by David Ferrer, cannot possibly finish in the top two of the group and move into the Saturday semi- finals.
Gasquet's record improve to 1-1 while Djokovic dropped to a pair of defeats in as many matches.
Rafael Nadal and year-end newcomer Ferrer were playing later in a battle of undefeated Spaniards.
Djokovic, worn out after a long season of 68 wins and 18 losses, was unable to make an impression on the Frenchman who squeezed into the last of the eight qualifying position for the year-end spectacular just days ago.
Gasquet began with a break in the third game and backed it up for 4-1 before losing his own serve a game later from an errant forehand.
But the French 21-year-old got it back for 4-2 and carried on to claim the opener. In the second Djokovic failed to lift as he lost serve two more times on the way out with a return wide down the line on first match point.
Gasquet, with a single title this season at Mumbai, will close his group campaign on Thursday against Ferrer.
Djokivic, who had his wisdom teeth removed last month and has never appeared to be fully recovered, struck 27 unforced errors while Gasquet moved through on 25 winners and five breaks of serve.
DPA