The Argentine Apertura championship leaders appeared set for their first win in Group Six when Santiago Biglieri put them ahead in the 29th minute from a rebound after Jose Sand's penalty was saved by Gustavo Dalsasso.
Sand had another effort blocked by Dalsasso two minutes later and then headed wide from Sebastian Blanco's cross before Everton, under former Chile coach Nelson Acosta, fought back in Tuesday night's game.
Roberto Gutierrez equalised on the break in the 52nd minute and substitute Jose Munoz scored the winner in injury time.
Lanus stayed bottom of the group with two points from four games while Everton joined leaders Guadalajara on seven points.
Apart from Boca Juniors, who have won both their games in Group Two, Argentine sides have managed only three wins in 12 outings between them in the tournament.
Colombian pair Independiente Medellin and America played out a goalless draw in Group Four, leaving Brazilian champions Sao Paulo and Uruguay's Defensor Sporting as clear favourites to progress.
Ecuador's Deportivo Cuenca went top of Group Two on goal difference by beating Venezuelan champions Deportivo Tachira 3-1.
Brazilian Rodrigo Teixeira scored twice for Cuenca who have six points and lead Boca on goal difference but have played two games more.
