Dibaba finished in 8 minutes, 45.05 seconds.
Dibaba seemed to pull up slightly in the last frenetic lap, but held on for victory in 8min 45.05sec, with Hassan cleverly shifting across the lanes to deny Muir.
Hassan trains as a member of the Nike Oregon Project.
Dibaba's final kilometre was 2:37 - around 7:52 pace - and the second half a very fast 4:04, which was 37 seconds quicker than the first half!
THE head of British Athletics saluted Andrew Pozzi as a "fantastic role model" after the Stratford hurdler was named co-captain for this weekend's IAAF World Indoor Championships in Birmingham.
Muir's success caps an extraordinary four days for the Scot, who made this championship a focus for the first half of 2018 as she will not compete at the Commonwealth Games in April in order to finish her veterinary studies. "This time yesterday I was in a taxi halfway down the M6".
With a grimace beginning to show on her face as the clock showed 8:14.61 at the bell, Dibaba had amassed a safe -but by no means unassailable- lead of roughly twelve metres on Hassan and Muir, but in their chase for the silver medal, the gap to Dibaba began to narrow.
Her team-mate Eilish McColgan came 10th in the 3,000m.
"The 2014 Commonwealth Games was an insight into just how well Scotland can play host to worldwide sporting events, and I am sure that Glasgow 2019 will be another step forward in cementing Scotland's status as a first-class deliverer of world-class sporting events".
That is not to take anything from Doyle, however. "It's not my preferred event so to do this is really incredible".
Giles' 800m controversy arrived after what he described as a "gut-wrenching" fourth place in the 800m, where Poland's Adam Kszczot added a global gold to a litany of silvers both indoors and outdoors in the past. "I'm very happy to be indoor champion for the third time".
The women's 60m hurdles looks likely to be one of the closest competitions of the Championships, and may quite possibly feature three USA athletes in the medal positions given the presence of world 100m hurdles record holder Kendra Harrison, Christine Manning and Sharika Nelvis, who leads the women's rankings this season after setting a 7.70sec national record at the trials in Albuquerque.
Officials disqualified Windle before reinstating him and later home fans witnessed more disappointment when medal hope CJ Ujah was disqualified for false-starting in the 60m semi-finals.
Muir went into this event as the double European indoor champion but her global record against tougher opposition had previously been less convincing. Those five or six-hundredths of a second could be crucial on Sunday.