O'Connor looked to be on course for gold having led from the off but was passed in the second half of the race by Emma McKeon of Australia.
Former Youth Olympic champion McKeown would not be pegged back after taking the lead off the penultimate turn that and took gold in a Games-record time of 1:55:57, with O'Connor taking silver.
That was to be just the start for the Bath swimmer, however, as she also picked up a silver medal in the 4x100m freestyle behind Australia.
O'Connor swam the lead off leg in a time of 54 seconds to keep England in touch with the strong favourites from Down Under.
Ultimately the Aussies proved to be too strong as they came home comfortable winners in a world record time of 3:30.98. There was also a record for the England team who smashed the British record.
Unsurprisingly, O'Connor was thrilled with her evenings work, saying: “It’s been a busy evening but I’m really happy with how it went, to win two medals is just fantastic.
“The first day was massively important to me, I knew it was going to be a big day and I’m glad to have got off to a good start.”
18-year-old O'Connor had earlier ensured she had another shot at a medal as she qualified for the 100m butterfly final with an impressive showing to win her semi-final.