Leicester City looked on course for their first Barclays Women’s Super League point of the season until Everton’s late free kick.
Substitute Hanna Bennison hit a 94th-minute set-piece, which may have been heading wide of the post until keeper Kirstie Levell got a touch on it.
Jemma Purfield earlier had a free kick pushed away by Emily Ramsey, while Katja Snoeijs nearly got on the end of an Izzy Christiansen cross for the hosts.