The final 400 metres saw Dibaba sprint clear, Hassan in second ahead of Muir as Obiri struggled.
The United States won nearly five times more medals than any other country at their home staging of the last International Association of Athletics Federations World Indoor Championships in Portland two years ago, and another medal-table-topping performance looks in prospect as the 2018 edition gets underway at Arena Birmingham tomorrow.
Hassan trains as a member of the Nike Oregon Project.
And the 27-year-old favourite made no mistake at the Arena Birmingham, streaking around the blue track for an unprecedented eighth Ethiopian victory in the last nine world indoor 3000m events, Kenya's Hellen Obiri the only blot back in 2012.
Genzebe Dibaba of Ethiopia, perhaps predictably, completed the double with a dominant 1,500m gold to add to her 3,000m title with a time of 4:05.27.
USA champion Shelby Houlihan, who trains with the Portland-based Bowerman Track Club, closed hard to take fifth in 8:50.38.
The World Indoor Athletics Championships start in Birmingham on Thursday.
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A veterinary student from Glasgow University who has prioritised her studies over athletics in... "I know I've been there or thereabouts - it was about time I got on the podium".
The Scot had looked in superb form throughout the indoor season and all went well with her preparation other than the weather necessitating a belated six-hour taxi journey from Glasgow as rail and plane options were scuppered.
Birmingham-based Robbie Grabarz, who shared the Olympic bronze medal in 2012 and took silver in Portland, is the local hope.
"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".
Chris O'Hare ensured Great Britain representation in the men's 1500m final on Sunday, while did David King (7.69 seconds) and British team captain Andrew Pozzi (7.53) moved into the men's 60m hurdles semi-finals.
McColgan was disappointed with her 10th place in 9:01.32. Britain's CJ Ujah was expected to challenge for a medal but blew it with a false start in his semi-final. "I've raced a lot indoors and done well, I'm in my comfort zone". The European Indoor silver medallist was plagued by injury problems during the winter and missed the recent British Indoor Championships with injury, so it was perhaps no surprise to see that he was looking rusty and lacked rhythm during a men's high jump that did at least provide an intriguing battle between Mutaz Esha Barshim and Danil Lysenko for gold. "It's not my preferred event so to do this is really incredible". Those five or six-hundredths of a second could be crucial on Sunday.
