The second seed from Yugoslavia, who received a first-round bye, fell in 70 minutes to Kremer in a shock 5-7, 2-6 second round defeat.
Sixth seed Magdalena Maleeva and eighth seed Amanda Coetzer also bowed out with the Bulgarian losing to Thai ace Tamarine Tanasugarn 3-6, 6-2, 2-6, and the South African going down to American qualifier Alexandra Stevenson 6-4, 0-6, 6-7 (3/7).
Stevenson will challenge another former number one, Monica Seles, who eliminated Belgian qualifier Els Callens 6-2, 6-3.
It was the first tournament of the season for 18-year-old Dokic, who skipped a series of events in Australia, including the Australian Open, after reportedly being worried about the media reception to her controversial father and coach Damir.
After trading service breaks in the eight and ninth games of the first set, Dokic had a disastrous game in the 12th starting it with a double fault — her fifth in the match, and ending with another at 15-40 to lose the set.
Overall, Dokic committed 11 double faults and was never able to recover her form after going 1-3 down early in the second set.
Dokic enjoyed her best season last year, capturing her first career title at the Italian Open in May and adding two more by winning in Tokyo and Moscow.
SINGLES 2ND RD:
Alexandra Stevenson bt Amanda Roetzer 4-6, 6-0, 7-6 (7/3); Tamarine Tanasugarn bt Magdalena Maleeva 6-3, 2-6, 6-2; Monica Seles bt Els Callens 6-2, 6-3; Anne Kremer bt Jelena Dokic 7-5, 6-2; Silvia Farina Elia bt Rita Grande 7-5, 6-4; Anna Kournikova bt Elena Dementieva (Rus x7) 7-6 (7/4), 7-6 (7/5)
QUARTERFINALS LINE UP:
Martina Hingis vs Tamarine, Sandrine Testud vs Farina Elia, Stevenson vs Seles, Kournikova vs Kremer
Doubles quarterfinals:
Silvia Farina Elia/Barbara Schett bt Monica Seles/Sandrine Testud 6-4, 7-5; Els Callens/Roberta Vinci bt Kimberly Po-Messerli/Nicole Pratt 2-6, 6-2, 6-2; Jelena Dokic/Iroda Tulyaganova bt Maria Emilia Salerni/Patricia Tarabini 6-2, 6-7 (3/7), 7-6 (8/6).
2ND ROUND:
Younes El Aynaoui (Mar x5) bt Stefano Galvani (Ita) 6-4, 6-3; Greg Rusedski (Gbr x7) bt Bohdan Ulihrach (Cze) 7-6 (7/5), 6-4.
1ST ROUND:
Michal Tabara (Cze) bt Goran Ivanisevic (Cro x3) 5-7, 7-6 (9/7), 3-0 rtd; Juan Carlos Ferrero (Spa x1) bt Julien Boutter (Fra) 3-6, 7-6 (7/5), 6-4; Max Mirnyi (Blr) bt Federico Luzzi (Ita) 6-0, 4-1 retired; Sarg Sargsian (Arm) bt Jiri Novak (Cze x6) 6-2, 3-6, 6-4.—AFP