Baines converted a spotkick won by Kevin Mirallas on 87 minutes to earn a deserved point for the visitors.
Blues were level barely a minute later as Nikica Jelavic headed home a tidy cross from Steven Pienaar.
The Latics then took the lead on 23 minutes as the dangerous Franco di Santo finished a sweeping counterattack involving Kone and Gary Caldwell.
After the break, Everton dominated play and deserved their equaliser - a goal for Baines against his former club.
TRIBAL ASKS: Is the partnership of Leighton Baines and Steven Pienaar the best in the country?