St Patrick's Athletic created the better of the chances in this Setanta Cup first round, first leg tie at the Tallaght Stadium but were unable to score as Glentoran held resolute.
Chris Forrester had a shot easily collected by Elliott Morris and had a strong penalty appeal turned down.
Killian Brennan saw a left-foot shot go wide of the post and Richard Gibson missed a good chance for the Glens.
Forrester drove over the bar and Morris dived low to save from Jordan Keegan.
The result puts the Irish Premiership side in a strong position going into next week's return leg at the Oval.