The 19-year-old runner finished just behind Team USA’s Athing Mu, also 19 – who set a new Americn record – and broke Kelly Holmes’ long-standing national record for the distance.
Hodgkinson ran 1m 55.58s to beat Holmes’ record of 1m 56.21s, set in Monaco in 1995.
At one point it looked as though Scotland’s Jemma Reekie would come home in third, achieving a second podium place for GB but despite setting a new personal best, the Scot was overtaken in the final stages by Raevyn Rogers of the USA, who took bronze by 0.09 seconds.
Great Britain's other entrant, Alexandra Bell, finished seventh in 1m 57.66s, also a PB for the Leeds-born runner.
Speaking afterwards a stunned Hodgkinson said: “I am pretty speechless right now. Kelly Holmes is a legend and I looked up to her.
"I have been speaking to her for the past couple of days and she is a lovely person.
"I want to thank my amazing team, my family who have made so many sacrifices for me.
"I think it is just one of those things where you know something like that is possible but whether it comes out you just don't know. It was such a good race.
"I wanted to put it all out there and I did that. It is going to take a couple of days to sink in."
Hodgkinson also paid tribute to winner Mu, adding: “I am not just 19, Athing is 19 too, so teenagers taking on the podium is incredible and hopefully we have got many battles ahead of us.”
Reekie added: “I knew I was in good shape, and I knew if I executed the race I could have been up there.
"I wanted to win, but sometimes you have to learn and Paris isn't too far away.
"I obviously wanted to do better, I am going to be hard on myself because I came here to win but I think I will look back in a few years time and realise how well I have done.”
Bell said she was “delighted” with a new personal best, saying: “I grabbed the opportunity with both hands and I just rolled with it.
"Racing hard for the last few days, I didn't know if I would be able to PB coming into the final, but my coaches coached me well and I got a PB out of it.
"I was so focused on not coming last, I wasn't even bothered about the time until I finished the race. When you focus on the race, the time will follow.”
Women’s marathon world record-holder Paula Radcliffe said on the BBC: “That look on Keely Hodgkinson's face, she has just seen the clock.
"She has just seen 1.55.88, a national record. Kelly Holmes' record has gone and what a way.
“My hands were on my head when she went on the inside with 200 metres to go, but the way she saw that path through and then closed out so strong.”
"Heartbreak for Jemma Reekie, [but] she didn't do anything wrong. She maybe just attacked a little too soon.”