Kenyan Beatrice Chebet finished second in 14:05.92 while Ethiopia's Ejgayehu Taye was third in 14:21.52.
"My focus today is world record," said Tsegay, who added that she would next try to run the distance under 14 minutes.
"...I’m very hungry in my mind."
Tsegay set a blistering pace from the start and was pushed by Chebet as the two rivals pulled away from the chasing pack.
She broke away from Chebet, who finished third in the distance at the Budapest World Championships, with about 800 metres to go, with the fans at Hayward Field on their feet as she raced against the clock.
The Tokyo bronze medallist was well ahead of the rest of the field as she powered through the final stretch, gritting her teeth with Kipyegon's mark within reach.
The crowd erupted with joy as she broke the tape at the same track where she collected world championship gold in the distance last year, and she offered a subdued celebration.
Tsegay, who won the 10,000 metres at the world championships in Budapest, collapsed to the track in sheer exhaustion before going to the stands to sign autographs.
The stunning performance trimmed roughly five seconds off of Kipyegon's previous record, set at the Paris Diamond League.
