Berdych defeated Fernando Verdasco 6-3, 7-5 while Tsonga was a 6-3, 6-4 winner over Guillermo Garcia-Lopez in second-round matches. Either can lock up one of eight invitations to the World Tour Finals by winning their next match.
Seven players are alive in the fight for the three unclaimed Tour Finals slots. No. 7-seeded Mardy Fish, like Berdych and Tsonga, can qualify by reaching the quarterfinals in Paris. Nicolas Almagro, Janko Tipsarevic, Gilles Simon and Gael Monfils have lesser chances of reaching the Tour Finals.
Berdych, seeded fifth, took his first step with five service breaks against Verdasco. The No. 6-seeded Tsonga had nine aces and no double faults in his win over Garcia-Lopez.
Ivan Dodig posted a 4-6, 6-1, 6-3 win over Fabio Fognini and earned a second-round match against world No. 1 Novak Djokovic. Jeremy Chardy advanced with Marcel Granollers retired in the second set. Chardy draws No. 2-seed Andy Murray in the next round.