Top seed Tsonga fired eight aces in a 6-2, 7-6 (8-6) win over Go Soeda of Japan and will play Sergiy Stakhovsky in Friday's quarters on the indoor courts at The Royal Lawn Tennis Club. Berdych had 11 aces in a 6-1, 6-4 besting of Jurgen Zopp of Estonia
Sixth-seeded Mikhail Youzhny blitzed Sweden's Patrik Rosenhom 6-0, 6-2, in just more than an hour Thursday and will play Berdych Friday.
The 30-year-old Russian chose to play in the Stockholm Open this week rather than the Kremlin Cup in Moscow, RIA Novosti said.
In other second round action, Sergiy Stakhovsky defeated No. 5 seed Feliciano Lopez 7-6 (7-5), 7-5 and seventh seed Marcos Baghdatis advanced 6-0, 3-0 when Colombia's Alejandro Falla retired.
Spaniard Nicolas Almagro meets former world No. 1 Lleyton Hewitt and Baghdatis plays Ricardas Berankis of Lithuania in other quarterfinal action.
The 2012 Stockholm tennis tournament champ will take home $113,000.