Czech fourth seed Berdych had to battle to overcome tall American Sam Querrey 6-2, 6-7 (3/7), 6-4. Tsonga, the fifth seed, saw off the challenge of former Australian Open finalist Marcos Baghdatis of Cyprus 6-2, 7-6 (7/2).
With four places in the London end-of-season showpiece still up for grabs, Tsonga, 27, and Berdych, also 27, each occupied qualifying positions going into their third-round ties.
World number one Roger Federer, Novak Djokovic, Shanghai Masters defending champion Andy Murray and the injured Rafael Nadal have already qualified for the eight-man field in London.
In a match containing eight breaks of serve, the powerful Tsonga struck 11 aces and Baghdatis was hampered by six double-faults.
Tsonga said he was happy with his game and focusing on the task in hand rather than on London.
"For the moment I think about this tournament," he said. "You know, I try to play my best tennis. After, of course for me London is a goal. But I also have another goal, to win some tournaments and try to beat the guy before me."
Berdych cantered through the first set of his match, breaking the 6 feet 6 inches (198 cm) Querrey twice. But the 22nd-ranked American levelled the match after coming out on top in the second set tie-break.
An early break for the Czech in the decider proved decisive as he wrapped up the set 6-4.
Federer, Djokovic and Murray are all in third-round action on Thursday, where a win for the Swiss 17-time Grand Slam champion will guarantee a 300th week in his career as the top-ranked player.
"I'm obviously excited," said Federer, who meets compatriot and 13th seed Stanislas Wawrinka. "It's a big number, even though 299 or 300 doesn't make a big difference for me. It's obviously a big match for me.
"Obviously it's not a final, so I'm not going to go in super-nervous about it. It's just more the difficulty of playing a good friend. That adds to the special occasion."
Even if Federer loses he will remain at number one after this week if Djokovic does not win the title in China.