After having a barrage of unsuccessful second-half attacks, Everton finally netted a warranted equaliser through Baines's 87th-minute spot kick.
Kone headed the Latics into a tenth-minute lead from Shaun Maloney's cross, although the Ivorian appeared to be in an offside position.
Everton's frustration at the officials was calmed when Jelavic equalised after he was fortunately found unmarked at the back post by Steven Pienaar's intended shot.
Di Santo restored Wigan's lead with a smart finish, stretching to beat Phil Jagielka to Kone's cross and convert from 15 yards.
The Toffees also had several penalty shouts turned down, before they eventually had a decision go their way when the referee adjudged that Maynor Figueroa had brought down Mirallas in the box.
Baines stepped up to convert from the spot, maintaining his 100% penalty record in the Premier League and earning Everton a point that keeps them third in the table.