A slice of luck had Basel up front after 17 minutes of action as Michel Aebischer put the ball in his own net but they went into the break behind after two strikes by Cameroon striker Jean-Pierre Nsame in the 41st and 44th minutes.
Before the hour mark, Okafor levelled proceedings with a well-struck shot from outside the area - his third goal in 16 league appearances this season and his first senior goal at the St Jakob-Park.
The 18-year-old, who received a caution in the first half, was subbed off late in the game.
With the stalemate, second-placed Basel  are still 21 points adrift table-toppers Young Boys  after 25 Swiss Super League encounters.
Two weeks ago, Okafor's progress in Basel's senior setup was rewarded with a contract extension.