Jones was eighth after the first heat, and recorded a slightly faster time in her second run. But she was well back on the pacesetters, Brit Mallory Franklin and Germany's Andrea Herzog.
Australian Jessica Fox, the favourite, had a few hiccups in the heats and qualified in fifth spot but is expected to hit her straps tomorrow.
Fellow Kiwi Callum Gilbert, at his first Olympics, missed a gate and lost 54 seconds in penalties in the first heat of the K1. He was much better in the second heat but was one of four to miss out on the 20-man semifinal.