Theo Archibald forced a good save from Exeter reserve goalkeeper Jack Bycroft early on – Bycroft made his first league start for City after Joe Whitworth failed a late fitness test.
Wareham could have put Exeter ahead when his 33rd-minute header bounced off the upright from a tight angle at the far post after excellent build-up play from Carlos Mendes Gomes and Danny Andrew.
The game was paused immediately after and an announcement on the public address system warned fans about their conduct after discriminatory comments were reported from the away end.
Exeter played some good passing football at times, and could have twice gone in front as the half ended in frenetic fashion – Ilmari Niskanen fired Charlie Cummins’ cutback from the byeline against the legs of an Orient defender while Reece Cole forced a superb save from visiting keeper Will Dennis.
The O’s immediately launched the ball upfield, and when Exeter centre-back Luca Woodhouse slipped Orient forward Ballard was clean through, but he scooped his shot over the bar.
Orient thought they had scored when Bakinson touched Archibald’s shot from a corner into the net, but the midfielder was offside, while he saw another effort cleared desperately by Johnly Yfeko eight minutes later after good hold-up play by Ballard.
Ballard – Orient’s 21-goal top scorer – began to get more influence on the game as he flashed an effort across the face of goal with 20 minutes left while the visitors were indebted to Dennis when he saved well from substitute Higgins three minutes later.
But, despite holding on for a point, Exeter’s day ended on a sour note when news filtered through that Blackpool had scored late on to go above them in the table.