Jankovic, meanwhile, looked set to make light work of 19-year-old Radwanska but, following treatment for an shoulder complaint, was broken when serving for the match at 5-2 and 5-4 before coming through a tie-break to seal the triumph.
"I had everything under control but the pain in my arm affected my shots," she said. "I started to feel it in the beginning of the second set.
"It is getting better but the other muscles are having to compensate for the injury. The whole arm is a mess.
"I worked so hard to win the match. I didn't want to play a third set so thankfully I won the tie-break."
The 2007 semi-finalist will play Carla Suarez Navarro after the 19-year-old qualifier beat Flavia Pennetta 6-3 6-2.
Pennetta failed to kick on from her shock win against Venus Williams in round three, converting only one of nine break-point chances as Grand Slam debutant Suarez, who stunned Amelie Mauresmo in the second round, reached the last eight.
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