After holding off two match points to win the second-set tiebreaker, Chan ran off three straight games to take a 5-2 lead in the third. However, Jankovic responded and tied the match at 5-5.
Chan held serve for a 6-5 lead, then got her third career win against a top-20 player in the next game when Jankovic hit a backhand long, ending the 3-hour, 13-minute quarterfinal.
Chan will next face the winner of the night match between top-seeded Marion Bartoli of France and No. 5 seed Christina McHale of the U.S.
Chan, ranked No. 161, trailed 6-5 and was two points away from losing in the second set when she forced the tiebreak.
The 20th-ranked Jankovic had two match points but Chan hit a backhand winner on the first and her Serbian opponent missed a backhand on the second.
No. 2 seed Dominika Cibulkova of Slovakia won 6-4, 6-4 over Poland's Ursula Radwanska.
Cibulkova reached her second semifinal of the season where she will face the winner between American Varvara Lepchenko and No. 4 seed Nadia Petrova of Russia.