Muir was the third home star to win a medal during a frantic evening in Birmingham after hometown racer Elliot Giles claimed a surprise bronze in the men's 800m and Eilidh Doyle clinched 400m bronze.
The high jump will be the first event of the world indoor track and field championships in Birmingham.
The 400m between 2000m and 2400m was run in 64.5 and Dibaba now had a small lead with Obiri, Klosterhalfen, Hassan and Muir the only likely challengers.
With five laps remaining, the serious racing began.
This was Dibaba's 4th indoor world title (3 straight at 3000m, plus a 1500m title from 2012) tying Meseret Defar for the most ever by a long-distance runner (Maria Mutola won seven 800m titles indoors).
She has always been earmarked as the leading home hope in the post-Mo Farah years, and that was supported with European indoor golds at 1500m and 3000m last year.
By the form book, Muir probably would have ranked third favourite for this; by force of will she got the silver, behind only Dibaba, who works under the controversial coach Jama Aden. Approaching the final turn, the deficit narrowed to a matter of metres but Dibaba gritted her teeth again and kept the pursuers at bay with a final circuit of 30.46 seconds.
The semi-finals in the women's 60m are due to take place at 6.50pm on Friday night.
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Reacting to her selection for the prestigious World Indoor Championships, Ciara Neville Tweeted: "Couldn't be happier to be selected to represent Ireland at the @iaaf_athletics World Indoor Champs in less than two weeks time". This is a great competition and the race was fantastic.
She said: "Yeah, I think so".
Hassan moved off the rail and nearly into lane three in an expedient bid to hold off Muir. Traditionally something of a 400m hurdles and 4x400m relay specialist - she won bronze as part of the GB 4x400m at the 2016 Olympics - Doyle set a season-best time to claim bronze.
Due to her final year university commitments, Muir could only travel down to Birmingham on the Wednesday, a task made hard by unseasonal snow and sub-zero temperatures which immobilized large parts of the British transport system.
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. "I just thought "stay with them, be controlled" and I came off with silver this time". "We couldn't see the bonnet, the windscreen wipers were freezing and it took six hours", she said.
USA champion Shelby Houlihan, who trains with the Portland-based Bowerman Track Club, closed hard to take fifth in 8:50.38.
Like Dibaba, Hassan and Muir, Houlihan will also be back in action tomorrow evening in the 1500m heats. "I just tried my best to the end of the competition".
The decoration of the two athletes required little more than an hour, but it all added up to quite a night for British Athletics, which arrived at the world titles with few dominant athletes but still rose to third in the overall medal table.