"But I tried hard and am feeling spent now, so I guess I couldn't have done much more."
It was the first time Joseph has bettered Hanlen this year as they compete for Olympic selection. Hanlen had previously won the domestic national series and also finished ahead in the opening two rounds of the world cup, with an eighth placing in South Africa and 18th in Belgium.
Hanlen had her problems on the starting loop, after being held up with a crash on the first lap and then with mechanical issues.
She fell back to 22nd place on the start loop and dropped back to 44th at the end of the first lap. The 32-year-old, who finished runner-up in the BMC Swiss Cup last week, gradually worked her way through the field to finish 26th, more than a minute behind Joseph.
"Unfortunately I got caught up in a crash on my first lap and had problems with my chain, which lost me a lot of time," Hanlen said.
"I tried to get back in the race but kept getting stuck behind slower riders on the single track to allow any real gains. I also dropped my chain again on the last lap, but I guess that's mountain bike racing. So it's not a great result today."
The battle moves to the fourth round of the world cup in France this weekend - the final round for Olympic qualification.
Results from the UCI mountain bike world cup in the Czech Republic today:
Elite women: Julie Bresset (FRA) 1:29.17, 1; Ireni Kalentieva (RUS) at 29 secs, 2; Katerina Nash (CZE) at 48s, 3. Also: Rosara Joseph (NZL) at 5:26, 22; Karen Hanlen (NZL) at 6:44, 26.