Kipyegon shaved almost an entire second off the previous mark of 3:50.07 set by Ethiopia's Genzebe Dibaba in 2015.
The world record completes the 29-year-old's collection of feats, adding to her two Olympic 1,500m golds and the 2017 and 2022 world titles, Commonwealth Games gold medal from 2014 and three Diamond League titles.
The Kenyan remained behind the pacemakers for the first half of the race before racing clear in the final 300m to finish well ahead of Britain's Laura Muir and Australian Jessica Hull, with her rivals crowding around to congratulate her after the race.
"I'm so happy for Faith," Muir said. "I would have loved to be closer to her. But for the first race of the season this is really decent. I have never gone through the first 800m as fast as today."
American Fred Kerley, who also won in Rabat last week, took the victory in a dominant 9.94 seconds, as Ferdinand Omanyala finished second in 10.05 with Trayvon Bromell third (10.09). Jamaica's Yohan Blake came in seventh.
Olympic gold medallist Jacobs did not compete due to a lingering back issue.
In the women's event, Ivorian Marie-Josee Ta Lou exploded off the blocks and crossed the line in 10.97 ahead of Germany's European champion Gina Lueckenkemper and Briton Imani-Lara Lansiquot.
Dina Asher-Smith, who won the world 200 metres title in Doha in 2019, pulled out in the build-up to the race.
"I feel a bit tired because I am jet lagged. The most important thing was the win and I got it," Ta Lou said. "This season, my main goal is to win every time I stand on the track."
American teenager Erriyon Knighton won the men's 200m in 19.89, while the Netherlands' Femke Bol set a meeting record in the women's 400m hurdles, surging away from the rest of the field to win in a world leading time of 52.43.
American Grant Holloway made up for his second-placed finish in Rabat with victory in the men's 110m hurdles.
Spaniard Mohamed Katir produced a lung-busting performance to win the 5,000m with a world leading 12:52.09, with world record holder Joshua Cheptegei coming in fourth.
Italy's Leonardo Fabbri and Andy Diaz gave the home fans packed into Luigi Ridolfi Stadium plenty to cheer as they claimed wins in the men's shot put and triple jump respectively, while compatriot Larissa Iapichino won the women's long jump.