The Blues needed first a point against the Tunisian giants and the first half suggested they may have a fight on their games, with ES Tunis standing tall to wave after wave of attack.
But two goals in first-half injury time settled the game and secured a last-16 clash with Benfica on Saturday night.
Enzo Fernandez floated a free kick from deep into the penalty area and Tosin Adarabioyo cushioned a header inside the far post. Two minuted later, Fernandez was provider again as Delap collected the ball with his back to goal, turned his man and then beat another before cooly slotting the ball beyond Ben Said in goal.