The draw extends Orient's unbeaten run to 13 games.
Orient, who face Arsenal in an FA Cup replay on Wednesday, were 2-0 down and had Harry Kane sent off soon after he pulled a goal back on 73 minutes.
But the visitors were undeterred and they grabbed a leveller after 88 minutes when Dean Cox floated in a free-kick after substitute Paul-Jose M'Poku was fouled by Town's Jamie McCombe. Smith rose highest in the six-yard box to subsequently send a header crashing into the net.
Huddersfield should have been on course for victory after going two goals up. They took the lead after just three minutes through a stroke of luck, the ball hitting referee Peter Quinn and Town's Lee Peltier pounced to put Benik Afobe in the clear.
Afobe drew Orient keeper Jamie Jones off his line and then squared for Jordan Rhodes to notch his 17th goal of the season from close range.
Huddersfield substitute Lee Novak, who replaced the injured Rhodes at half-time, hit a sweet half-volley from Anthony Pilkington's cross after 49 minutes that should have sealed victory, but instead Orient roared back to claim a deserved point.