Fast-finishing Mary Moraa takes 800m gold in Budapest
Olympic and defending champion Mu set the pace from the gun but, having barely run the distance this season, was never able to open a gap.
Moraa stayed on her shoulder throughout and delivered her trademark final 100 metres burst to move past the American to triumph in 1:56.03, leaping and punching the air in celebration as she crossed the line.
Hodgkinson, just as she did in Eugene, tried to find a way through on the inside but though this time she got past Mu, was outsprinted by Moraa and had to settle for a second successive silver in 1:56.34, having also taken silver, behind Mu at the Tokyo Olympics.
Mu, whose participation had been in doubt until a few weeks before the championships as she flirted with the 1,500 metres took bronze in 1:56.61.
"After bronze last year I wanted to improve and I have," Moraa said. "Everyone in the final was so fast I knew I would have to have a fast finish. I came from a long way behind but I managed to do it."
"Another podium, another medal," said Hodgkinson, the European champion. "It's not gold but it's not bronze.
"I did think I would get through on the inside but the line came a bit quicker than I thought.
"I was really up for it, I really believed I was going to win. It was a different order this year, it might be again next year. In Olympic year everyone brings even more of their A game. All I can do is aim for gold again. One of these days I will get the top spot."
Mu said: "I came here to Budapest with no big expectations and now I am really grateful for this wonderful bronze medal.
"I wanted to slow the pace a little bit since I knew it would be a killer finish. Once I was overtaken from that point I just wanted to finish on the podium."