The race started at a relative jog with Muir ahead in 36 seconds with McColgan second and Dibaba at the back of the field of 14.
Unbeaten over 5000m outdoors in 2017, Obiri finished fourth in 8:49.66, one place ahead of reigning U.S. indoor 1500m and 3000m champion Shelby Houlihan, who ran a strong last lap to finish fifth in 8:50.38, overhauling Ethiopia's Fantu Worku (8:50.54) and Klosterhalfen (8:51.79) in the final 200m.
Eilidh Doyle got the evening session off to a winning start for Great Britain winning bronze over 400m with a great performance, while Zoey Clark finished sixth in her first individual world final.
Muir said trackside: "I just got a taste of it after the 3,000".
"I thought if I could medal in one event it would be a great achievement".
"This adds another accolade to my collection which is fantastic", said Doyle, who has also won medals at the outdoor world titles.
"I was very close to silver in the 3000m so I knew I just had to go for it this time". Other British athletes who have ambitions of adding to the medal tally are Katarina Johnson-Thompson, Andrew Pozzi in the 60m hurdles and both Dina Asher-Smith and CJ Ujah over 60m.
It appeared the home nation may have won another bronze on a Saturday packed with controversy when Elliot Giles, 23, was briefly promoted from fourth place in the men's 800m, when American Drew Windle was disqualified.More news: Tony Carr struggles as Penn State's run ends in Big Ten semifinals
These upgrades follow the disqualification of results of the original medallists after they were sanctioned for violating anti-doping rules. Both will open their campaign in Birmingham on day three of the championships, on Saturday.
Muir will miss April's Commonwealth Games though as she studies for her final veterinary exams at the University of Glasgow in May.
She undertook a six-hour taxi journey to get to Birmingham on Wednesday as Britain's roads felt the impact of the freezing temperatures and heavy snow.
London was her last competition until she came out and vaulted a very respectable 4.70m of a short 10-stride run-up in Hastings in January in her first competition.
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.
Dibaba never looked under real threat but Muir held Hassan off, in the same way the Dutch athlete did to her in beating her to silver in the 3,000m. I did not intend to lead, just to stay out of trouble and then it was a case of following the pace and trying to run on the inside but stay in contact and wait for the move. It was a stunning piece of running by all three women, particularly Muir.
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.
Sprinter Sean Safo Antwi met the entry standard for the IAAF World Indoor Championships Birmingham 2018 after clocking 6.56s in the men's 60m to meet the IAAF's qualifying mark of 6.63s.