Tsonga is now 295 points behind Spain's Pablo Carreno Busta who holds the final qualifying spot. The two remaining places for the season-ending event will be decided in the Paris Masters, the final tournament of the regular season, which starts on Monday.
Pouille, who has won titles in Budapest and Stuttgart this year, stretched the world number 15 right from the start with a barrage of aggressive baseline shots.
After saving two break points, Tsonga's only double fault of the match helped Pouille to take a 3-1 lead and the 23-year-old tightened his grip on the contest to cruise to a one-set lead.
A decisive break in the fifth game of the second set gave Pouille, who fired 17 winners in the match, the advantage at 3-2 and he did not look back.
Pouille sealed the win after Tsonga's backhand hit the net on match point and he became the first player to win an ATP title on grass, clay and hard court this year.
(Reporting by Shrivathsa Sridhar in Bengaluru; Editing by Clare Fallon)
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