There was a discussion with officials after six athletes cleared 5.50m with their first jump and it was decided that 13 athletes could progress instead of the usual 12.
Speaking to BBC Sport, Lewis, 26, said: "One jump made the final today which is just amazing.
"Morning sessions are not easy and in pole vault you have to be awake.
"The first box is ticked and now I'll look forward to Friday (the final) and hopefully win a medal."
Lewis's personal best of 5.82m is a British record and he will probably need to better it to be in with a chance of a podium place.