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The hosts had created the better chances in the first half but were unable to force a breakthrough as Town defended well.
And after Clarke was sent on, he broke the deadlock with his first opportunity to put the visitors ahead to the delight of their 1,200-plus travelling supporters.
But they were not quite able to hold on for a third consecutive victory as the hosts struck back from the penalty spot in added time, with Lee Angol stepping up to rescue a point from 12 yards.
Leyton Orient: Sargeant, Turley, Brophy, Coulson (C), Happe, Kyprianou, Wilkinson, Wright, Marsh, Maguire-Drew, Angol.
Subs: Janata, Ekpiteta, Judd, Clay, Dayton, Harrold, Sotiriou.
Town: McKeown (c), Hendrie, Davis, Pollock, Glennon, Whitehouse, Hessenthaler, Clifton, Rose, Vernam, Wright.
Subs: Russell, Öhman, Starbuck, Buckley, Hewitt, Clarke, Cardwell.
Attendance: 6,248 (1276)
Referee: Will Finnie
Possession: Leyton Orient 55%-45% Town