Neville, coached by Noelle Morrissey, finished in third place at the Irish Life Health National Indoor Championships in the Sport Ireland National Indoor Arena in Abbotstown last month in an impressive time of 7.35 seconds.
Dibaba held her form in covering that last circuit in 30.44 but even faster were her two pursuers.
Thomas-Dodd created history on the day by becoming the first Jamaican woman to win a global medal in a throwing event.
Britain's Eilidh Doyle had only advanced to the 400m final after she was upgraded to second in the semi-final thanks to a lane violation disqualification for Switzerland's Lea Sprunger.
BIRMINGHAM, ENGLAND (01-Mar) - Genzebe Dibaba of Ethiopia became the third athlete to win the women's 3000m title at the IAAF World Indoor Championships on at least three occasions in an exciting climax to the first day which had a sparse but enthusiastic home crowd cheering the narrow but growing possibility of a home victor in Laura Muir on the last lap. I feel like a year ago I had a really great season but unfortunately I didn't make the team.
For Muir, the decision to double up over 1500m and 3,000m took serious consideration, particularly with the demands of 12-hour night shifts and course work towards her veterinary science finals at Glasgow University. She had maybe not looked at her best this winter but still easily topped the 2018 world 1500m and 3000m lists and was bidding to win Ethiopia's eighth gold in the last nine editions where they have won a total of 14 medals.
Great Britain's other representative in the race - Eilish McColgan - came 10th, stating: "I'm really disappointed".
It was the Russian (or ANA - Authorised Neutral Athlete), Lysenko, who maintained his unbeaten start to 2018 by taking gold with success at 2.36m on his third attempt, while Barshim, the 2014 World indoor champion, failed with three attempts at the same height.
"It was a tactical race and I controlled all the competitors. Tomorrow in the 1500m I will try to get gold medal number two".
"Being so close to silver [in the 3,000m], after that race I knew I was in similar shape to Hassan and I could get the silver and beat her". I had to dig in on that last lap.
"I felt so much more relaxed here than I was at Sopot four years ago when the pressure got to me". "I stayed calm and made it through". I'm really excited and feel well prepared.
It is impossible to overstate the current quality of women's middle-distance fields. So to come out with a medal in that situation is fantastic.
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