It took a sublime finish on 59 minutes from Blackman to break the deadlock. The striker collected a pass 25 yards from goal, brought the ball onto his left foot and curled his shot past the right-hand of O's keeper Ryan Allsop.
The visitors would have been happier with a stalemate at half-time having been forced to replace keeper Mark Howard in the 12th after he slipped taking a goal-kick and was stretchered off to be replaced by George Long.
Following Blackman's goal, the visitors dictated matters although they were indebted to 18-year-old Long for an outstanding save on 70 minutes to maintain their advantage after Orient mounted their only serious attempt of the afternoon.
Lee Cook delivered a cross into the box where Kevin Lisbie headed the ball powerfully towards goal but Long produced a brilliant save from point-blank range.