Tsonga, who ended the hopes of home favourite Ruben Bemelmans in the semi-finals, beat Argentina's Schwartzman 6-3 7-5 to boost his chances of qualifying for the AT P Finals in London in November.
Like Dimitrov and Anderson, David Goffin is chasing a Finals berth but the top seed at the European Open suffered a shock exit in his quarter-final against teenage qualifier Stefanos Tsitsipas.
Del Potro, who survived a marathon semi-final encounter with Fernando Verdasco on Saturday, needed just 83 minutes to run out a 6-4 6-2 victor and secure his first tournament of the season. Dimitrov was looking to add to his titles in Brisbane, Sofia and Cincinnati this year.
Grigor Dimitrov needs to wait a bit longer to seal his place in the season-ending ATP Finals in London. This marks Tsonga's first finals appearance since winning the Open Parc Auvergne-Rhone-Alpes Lyon title in May.
At the Kremlin Cup in Moscow, Bosnian sixth seed Damir Dzumhur will take on Ricardas Berankis from Lithuania in the final after wins over Mirza Basic and third-ranked Adrian Mannarino respectively. In the third round, tonight the number 1 Bulgarian defeated with 6:3, 6:4 the German-born Russian representative for just over an hour. He is expected to climb from No. 38 to at least No. 33 when the latest rankings are released Monday.