Kanepi took a tight 3-6, 7-6 (8-6), 6-3 decision over Kerber before rains hit at Wimbledon and play was suspended.
No. 8-seeded Petra Kvitova trailed 25th-seeded Ekaterina Makarova 3-6, 6-2, 2-1, with Makarova to serve, when play was halted in their third-round match. Kvitova is the highest-seeded player remaining in the lower half of the draw.
Kerber was playing a second-round match carried over from Thursday when she met Kanepi. Kerber had more breaks (4-3), more points won (95-91) and fewer unforced errors (17-27) but fell when she was unable to solve Kanepi's serve in the third set.
Flavia Panetta pulled off a smaller upset, ousting 29th-seeded Alize Cornet 0-6, 7-6 (7-4), 6-2.
No. 15-seeded Marion Bartoli stands to be the highest seed in her half of the draw if Kvitova fails to come back in the third set. Bartoli beat Camila Giorgi 6-4, 7-5 Friday.
Local favorite Laura Robson, given a Center Court stage, advanced to the third round with a 6-4, 6-1 win over Mariana Duque-Marino on the strength of five breaks.
U.S. player Alison Riske came out on top of another second-round match between unseeded players, defeating Urszula Radwanska 4-6, 6-3, 6-4.
Also Friday, 19th-seeded Carla Suarez Navarro beat Eugenie Bouchard 7-5, 6-2, No. 20 Kirsten Flipkens posted a 6-4, 6-2 win over Vesna Dolonc and Karin Knapp got by Michelle Larcher de Brito 7-5, 6-2 in third-round matches.