The two sides finished the Apertura, the first of two championships played in the season, with 39 points from 17 games after Saturday's games.
Goal difference is not used to decide the title so they will meet on Tuesday at Santiago's Estadio Nacional.
Universidad Catolica cruised to a 2-0 win at Union La Calera and were on the point of clinching the title as O'Higgins trailed 3-2 at Rangers with 15 minutes to play.
However, Osman Huerta equalised in the 78th minute and Rangers had Sebastian Luna sent off two minutes later.
Rangers goalkeeper Nicolas Peric gave away a penalty and was sent off and Pablo Calandria fired home his second penalty of the match in the dying seconds to complete a 4-3 win.
O'Higgins have never won the title while Universidad Catolica have been crowned 10 times, making them the country's third most successful club behind Colo Colo and Universidad de Chile.