Jankovic, a former world No. 1, overcame 10 double faults in a sloppy first-round match to get by Britain's Laura Robson 6-4, 7-6 (10-8) on the indoor hardcourts at Copenhagen's Farum Arena.
She now goes on to face Russian wild card Yulia Putintseva in the next round.
Meanwhile, Kanepi moved into the quarterfinals, winning a third-set tiebreaker against Timea Babos en route to a 7-5, 4-6, 7-6 (7-2) triumph in a second-round match-up.
Each player dropped serve five times in 17 games, including twice in the third set, before Kanepi took the decisive tiebreaker.
No. 6-seeded Mona Barthel had an easier time in her second-round match, taking out Alberta Brianti 6-3, 6-2. She won two-thirds of the points on serve and more than half when receiving.
Also advancing to the quarterfinals were Alize Cornet, who beat Patricia Mayr-Achleitner 6-2, 2-6, 7-5, and Petra Martic, who topped qualifier Johanna Konta 6-2, 6-3.
No. 3-seeded Jelena Jankovic posted a 6-4, 7-6 (10-8) win over Laura Robson and Bojana Jovanovski stopped Stefanie Voegele 6-3, 6-4 in a pair of first-round matches.
LGBT community has 'bullied the American people': Bachmann
Beautician charged with giving client fatal silicone butt injection