The 24-year-old, unbeaten in the seven-sport event since 2002, bettered her personal records in the 100-metre hurdles and the high jump to collect 2,273 points, 51 points clear of Britain’s Jessica Ennis.
Ukraine’s Lyudmila Blonska stood third with 2,219 points with the shot put and the 200-metre to be contested later Saturday and the long jump, the javelin and the 800m on Sunday.
Klüft, the reigning Olympic champion who has hinted Osaka could be her last heptathlon at major championships, finished second behind Ennis in the 100m hurdles in 13.15sec, tying her personal best time.
Ennis, 21, a usual leader in the 100m hurdles and the high jump, also lowered her personal record to 12.97sec.
Klüft cleared 1.95m in the high jump, beating her personal best by one centimetre and immediately sprung back with clenched fists and a big yell.
Blonska, the world indoor champion who narrowly lost to Klüft by 6,681-6,626 points at the IAAF Combined Events Challenge in Gotzis in May, was fourth behind another Briton Kelly Sotherton in the hurdles.
But she cleared 1.92m for the second best high jump to trail close behind Klüft overall.
Ennis’ high jump attempts ended at 1.89m and Sotherton’s at 1.86m.