In a first half of very few openings, Jose Baxter spurned the best chance for the home side when he failed to hit the target after just 60 seconds.
It was a miss that was eventually punished with 38 minutes played during what was a rare venture forward from the away side.
It was a goal that sparked a second-half onslaught from hosting United as they laid siege to the Orient goal.
With 50 minutes played, the ball dropped for James Wallace just one yard from goal, but the midfielder sent his effort over the crossbar.
Nigel Clough's side continued to pour forward as the half progressed and their chances of claiming a share of the spoils were boosted 15 minutes from time when Orient veteran Jobi McAnuff was handed his marching orders for a second bookable offence. It was the first time that the midfielder had been sent off during his long career.
It seemed that the away side were going to hold out despite their numerical disadvantage, but United made their domination count in dramatic circumstances.
First Paddy McCarthy marked his home debut by bundling the ball in from close range, then, 60 seconds later, Marc McNulty rose highest in the second minute of injury time to head in what he thought was the winner.
However, in the 99th minute, Vincelot met a Jack Price corner and was able to power his header into the net to earn an unlikely draw for the managerless visitors.