Muir was 10 metres behind Kenya’s reigning world and Olympic champion, 29, heading into the final lap.
And Kipyegon streaked clear to win in 3 minutes 49.11 seconds, breaking the 3:50 barrier for the first time, while Muir ran a season’s best of 3:57.09.
Ethiopia’s Genzebe Dibaba set the previous record of 3:50.07 in 2015.
Ireland’s Ciara Mageean also ran a season’s best time as she finished fourth in 4:00.95.
Kipyegon has won both world and Olympic gold on two occasions but this is the first time she has broken the world record.
She now holds the first and third fastest times in history, running her previous best of 3:50.37 last August.
Former 200m world champion Dina Asher-Smith had to pull out of the women’s 100m moments before the race after suffering from cramp in the blocks.
“Other than that all good, but I didn’t want to risk anything today,” she said on social media.
“Frustrated as I was so excited to race, but had to make a sensible call for the bigger picture.”
Fellow Briton Imani-Lara Lansiquot finished third in 11.16secs, behind Marie-Josee Ta Lou of the Ivory Coast (10.97) and Germany’s Gina Lueckenkemper (11.09).
World champion Fred Kerley was again denied a meeting with Olympic champion Lamont Marcell Jacobs in the men’s 100m as the Italian had not recovered from the back problem that forced him out of last Sunday’s Diamond League meet in Rabat.
Kerley remains unbeaten this season, winning in 9.94 from Kenya’s Ferdinand Omanyala (10.05) and fellow American Trayvon Bromell (10.09).
Meanwhile, Erriyon Knighton breezed to victory in the men’s 200m with a season’s best of 19.89.
The 19-year-old American, who holds the under-18 and under-20 world records, finished well clear of Trinidad and Tobago’s Jereem Richards (20.28) and Aaron Brown of Canada (20.31).
