Scunthorpe were quickly out of the blocks and inside the opening two minutes Wayne Graves forced Glen Morris to finger tip a long range effort over the top and then Steve Torpey's left foot drive was whipped over the bar.
However the Iron didn't have to wait long before they drew first blood. Matthew Sparrow collected a throw in to pivot on the edge of the box and volleyed home a right foot shot in the seventh minute.
A poor header by Leyton Orient's Billy Jones fell to Sparrow and again Morris came to the rescue with another finger tip save.
Leyton Orient came into the reckoning and a free kick by Ciaran Toner caught the home side flat footed but Andy Scott was unable to make contact.
The home side hit back strongly and Orient skipper John Mackie cleared off the line from Paul Groves and further opportunities fell to Steve Torpey and Steven MacLean and then Torpey hooked a long range effort over the advancing Morris, but it fell the wrong side of the bar.
The Londoners made a bright start to the second half and Toner found space to fire in a right foot shot which Evans palmed over. Then they were denied in the 63rd minute when Jones pulled the ball back and Wayne Purser beat Evans to crash a shot against the foot of the post.
However, Purser did eventually claim the equaliser when he clipped home a close range equaliser following substitute Jabo Ibehre's low cross.
Scunthorpe almost snatched the points in the last minute when substitute Paul Hayes broke free only to hook a good chance over the bar.