Ballanger beat Germany's Annett Neumann 2-0 in the best-of-three matches final to add the world title to the Olympic gold medal she won in July.
France also took third place in the sprint, Magali Faure defeating ex-world champion Tanya Dubnicoff of Canada 2-0.
Ballanger, 25, will be aiming to complete a track double when she defends her 500 metres time trial title on Saturday.
The other final of the night, the women's 24-kms points race, also ended in success for the reigning champion.
Russia's Svetlana Samokhalova fought off a spirited challenge from American Jane Quigley to take the title for a second year.
Russia, the only nation to have two riders in the field, made full use of their numerical superiority.
Goulnara Fatkoullina helped Samokhalova to build an unbeatable points lead before snatching the bronze medal.
Quigley, a former medallist in the points event, led the race at half distance. ``I went so close this time, but having two riders certainly gave the Russians an advantage,'' she said.
The first six riders lapped the field, which left former world champion Ingrid Haringa of the Netherlands down in seventh place despite having the second highest points score.
Olympic champion Nathalie Lancien of France also missed the winning attack and finished a disappointing 10th.