Djokovic rushed through the first set then lost his serve twice in the second before winning the second-round match.
Florian Mayer of Germany also made the last eight.
Radwanska, coming off a loss in the final of the Japan Open on Sunday, struggled in her first matchup against the Spaniard. Radwanska broke six times and lost her own serve seven times.
Jankovic fell apart after leading 5-2, going out to Carla Suarez Navarro of Spain 7-5, 6-4.
"Jelena is always difficult to play, but I played well," Suarez Navarro said. "She always fights a lot, and I'm happy to have finished it off."