Cheptegei finished the 5,000m in 12:35.36 to break a record that had stood for 16 years, set by Ethiopian Kenenisa Bekele.
The race was also the 23-year-old's first on the track of the season, with the majority cancelled or postponed amid the Covid-19 global pandemic.
Johnson-Thompson finished sixth in the high jump, with a height of 1.84m, far behind her personal best of 1.98.
The gold and silver medals went to Ukraine with Yaroslava Mahuchikh finishing first and Yuliya Levchenko just behind her compatriot.
The 27-year-old finished ahead of fellow Scot Jemma Reekie, who came fourth behind Ireland's Ciara Mageean, as both of them ran personal bests.
British hopeful Adam Gemili ran a season's best time of 20.68 in the men's 200m final, but it was not enough to trouble American brothers Noah and Josephus Lyles, who took gold and silver.
Andrew Pozzi equalled his personal best in the 110m hurdles to claim silver with a time of 13.14.
The 28-year-old finished just three hundredths of a second behind first-placed Spaniard Orlando Ortega.
Laura Weightman set a new personal best in the women's 500m, finishing in third place with a time of 14:35.44, while Kenya's Hellen Obiri, the current world champion, took gold.