A pretty uneventful first half saw the Bees take the lead in the 13th minute when a swift attack led by Albert Adomah saw him find striker John O'Flynn.
Encouraged to run by the Dagenham defence, he fired in a low strike which - aided by a slight deflection - beat Daggers goalkeeper Tony Roberts at his near post.
The visitors didn't offer much in reply, although Ben Strevens should have made more of his chance but he headed wide from Sam Saunders' cross.
However, Barnet's Israeli goalkeeper Ran Kadoch had precious little to do, while at the other end, 40-year-old Paul Furlong, making his home debut, was proving to a be a threat for the visiting defence, although he failed to create any noteworthy chances.
Barnet felt they had a good shout for a penalty just after the restart when claiming Anwar Uddin handled Michael Townsend's cross.
They were even more aggrieved not to have been awarded it as, with 64 minutes on the clock, Dagenham were back on level terms.
A long goal-kick forward from Roberts led to hesitancy in the Bees defence, Danny Foster challenged Kadoch for the ball with the latter's weak punch presenting Mark Nwokeji with the simple task of steering the ball into an open net.
It got worse for the home side when, with just under 20 minutes left, Barnet were reduced to ten men when Michael Leary picked up his second yellow card of the match.
However, Dagenham weren't able to capitalise on their one-man advantage as Hendon's side held on for a point.