Orient opened strongly and big striker Jabo Ibehre saw a shot charged down and the Iron responded with Lee Featherstone's header being turned over by Barrett.
Scunthorpe might have gone ahead after 14 minutes. Martin Carruthers did well to turn the ball back from the by-line for Steve Torpey, who was off-target from six yards.
Both sides showed a keen desire to attack but when the O's gained a free-kick 30 yards out Matt Lockwood fired over the top of the stand and at the other end Wayne Graves tried a 25-yard left-foot shot which was saved easily.
The home side found themselves stretched when Ibehre got forward but Tommy Evans was not troubled.
Scunthorpe went ahead on 27minutes, Torpey flicked the ball on for Matt Sparrow, who lifted the ball over a defender and followed up to drive home a right-foot shot.
Andy Dawson did well to block an effort from Ibehre, but Orient grabbed a 39th minute equaliser when Dean Smith dived low to head home.
The home side opened strongly in a shrouded stadium and in the second half both Sparrow and Torpey were on-target without making their efforts count.
Scunthorpe went close to increasing their lead when Torpey got in a strong header against the post, but Barrett got down to turn the ball away.
However, Scunthorpe's extra class saw them grab a second and the winner in the 67th minute when Ian Kilford drove the ball home for his first goal for the club in some style.