The 23-year-old's time of nine minutes and 0.48 seconds eclipsed Meseret Defar's mark by almost six seconds.
Dibaba, sister of three-time Olympic champion Tirunesh, already owns the world 3,000m and 1500m indoor records.
Elsewhere, British indoor champion James Dasaolu won the men's 60m despite suffering an injury during the race.
The 26-year-old Londoner posted the quickest time of the year in the heats, clocking 6.47 seconds, but his 6.50-second victory in the final was marred by an injury sustained in the final 10m.
Dasaolu, a medal hope for next month's World Indoor Championships, later said he suspected it was cramp after initially fearing a hamstring problem.
"My left leg felt tight at about 40-50m. I think it's cramp, but I'll go and see the doctors and see what they say," said Dasaolu, who was clutching his left leg while crossing the line.
British Athletics medical staff said the sprinter would be assessed further on Monday.
It was the final race of the day, however, which drew a standing ovation from a sell-out crowd who applauded Dibaba's incredible feat.
The Ethiopian was expected to better compatriot Defar's time of 9:06.28, set in Prague in 2009, and did so convincingly, despite slowing towards the end.
Her feat is a world best rather than a world record as the two miles race is not an official world record event.
Dibaba, who is also the sister of Olympic silver medallist Ejegayehu Dibaba, broke the 3,000m world indoor record by 13 seconds on 6 February. That record in Stockholm came just five days after she had set the 1500m world indoor mark in Karlsruhe, Germany.
It was a photo finish in the women's 60m, with Murielle Ahoure taking victory despite 100m world and Olympic champion Shelly-Ann Fraser-Pryce crossing the line in the same time of 7.10 seconds.
There was a personal best for Scotland's Laura Muir, who held off a late challenge from Sifan Hassan of the Netherlands to win a thrilling 1500m in 4:05.32.
"I'm so happy. I knew I was in good shape and that it was a matter of running a good race," said Muir, now second behind Dame Kelly Holmes on the UK all-time women's 1500m indoor list.
Olympic champion Greg Rutherford, who ruptured a hamstring in 2013 and failed to qualify for the World Championships final in Moscow, came third in his first indoor long jump competition in four years.
His best of 8.00m was not enough to beat world champion Aleksandr Menkov (8.14m).
Olympic bronze medallist Robbie Grabarz (2.27m) could only finish third behind winner Erik Kynard (2.34m) in the men's long jump.
Holly Bleasdale, the European indoor champion, won the women's pole vault by 10cm. The 23-year-old from Preston could not improve on her winning height of 4.71m, despite three attempts at 4.77m.