Jones was the sixth paddler down the course in the top-10 final, after a qualifying in fifth with a slick 97.84 semifinal performance.
She was just outside Tercelj's 94.27 time, set the run before her in the final, with her only real slip running low into the upstream Gate 14 and needing a few extra strokes to get through.
She then had to watch the last four paddlers attack her time, with only defending champion Fox getting ahead of her.
"I had a few tiny errors and when there's only half a second between first and third, I'm starting to think about those errors a little bit and kick myself but overall, I'm really happy.
"It was quite nerve-wracking — I was in third position and Ricarda Funk was the last person to come down and she's a German powerhouse and just so fast.
"I just couldn't even watch — I just had to hold my breath."
Funk picked up a touch early in her run, however, and eventually finished fifth, leaving Jones jubilant but trying to keep things in check.
"There's cause to celebrate but I have C1 (overnight NZT) so I'll be trying to calm down and just prepare as well as possible for that."
By making the final, Jones also guaranteed her selection for next year's Tokyo Olympics, which will be her fourth appearance at the Games, joining the likes of board sailor Barbara Kendall (who attended five), table tennis stalwart Chunli Li, discus thrower Beatrice Faumuina, runner Lorraine Moller and shotputter Valerie Adams as quadruple Olympians.