Despite the hosts dominating the opening exchanges, with both Matt Tubbs and Wes Thomas testing Orient goalkeeper Lee Butcher, it was the visitors who opened the scoring through Kevin Lisbie in the 16th minute.
Ryan Dickson crossed a hopeful ball to the far post where the evergreen Lisbie found space to manoeuvre a low shot, which goalkeeper Darryl Flahavan spilt into the net.
The Cherries replied in the 33rd minute, when Thomas’ forward pass fortuitously rolled past Tubbs to the unchallenged Marc Pugh, who applied a neat finish to equalise.
An action-packed first 45 minutes was followed by a second half of few openings.
With 15 minutes to play and on a rare outing inside the Cherries’ penalty area, Smith rose above his opponents to head in Jonathan Tehoue’s precise delivery.