The 23-year-old, who was competing in just her fifth half marathon, clocked splits of 30:05 and 45:37 to improve the 10km and 15km world records.
But a modest Jepkosgei, whose previous best time was 1:06:08 in this year's Ras Al Khaimah Half Marathon, said:
I didn't know I would break the world record today. I only wanted to improve my time. This is a surprise for me. The conditions were good for me because I'm used to training at this time of day, in the morning.
Defending champion Violah Jepchumba of Kenya finished second in 65:22, with Fancy Chemutai third.
Jepkosgei was pushed to her limits by Jepchumba as the pair were separated by one second at the 10km mark, both well inside the previous record of 30:21 set by Paula Radcliffe in 2003.
However, Jepkosgei began pulling away from Jepchumba as her lead grew to three seconds at 15km and she crossed the line with 64:52 on the clock to shave 14 seconds from the world half-marathon record set this year by compatriot Peres Jepchirchir.
Ethiopia's Olympic 10,000m bronze medallist Tamirat Tola won the men's race in 59:37. Kenyans Josphat Tanui and Geoffrey Yegon were second and third.
Read the original article on Eurosport: Jepkosgei smashes three world records at Prague Half Marathon