New Albion boss Russell Slade took charge for the first time and his side included five debutants, with one of them playing a key role at both ends.
Matt Heath scrambled the ball home in the 17th minute after goalkeeper Jamie Jones had failed to deal with a free-kick conceded by centre-back Jordan Spence.
But Orient equalised from the penalty spot through striker Scott McGleish in first-half added time after Heath had upended striker Simon Church.
McGleish hit the framework and midfielder Thornton had a goal disallowed for offside during early second-half Orient pressure.
Just when a draw looked likely, Thornton weaved his way in from the left and found the top corner with a fine right-footed shot.