The home team held on for a deserved draw after seeing their early lead cancelled out by a net-busting equaliser from Barnet striker Anthony Thomas in first-half stoppage time.
Sam Saunders went close for the home side in the tenth minute when he fired an audacious volley straight at Bees keeper Lee Harrison from the edge of the box.
Harrison was called into the action again in the 15th minute when Dagenham midfielder Sam Sloma stung his palms with a powerful 25-yard free-kick.
Barnet presented the home side with a gift in the 20th minute when Daggers striker Ben Strevens poked the ball home after a mix-up in the box between Harrison and defender Ismail Yakubu.
Saunders almost made it two a minute later when he thundered a shot narrowly over after linking well with Sloma.
Barnet's first real chance fell to striker Adam Birchall in the 31st minute when he forced an athletic save out of keeper Tony Roberts from point-blank range after sneaking behind the Dagenham defence.
The visitors threw men forward and grabbed a deserved equaliser in first-half stoppage time when Thomas burst Roberts' net with a thunderbolt 30-yard free-kick.
The Bees came flying out of the blocks in the second half with Yakubu powering a header inches over the crossbar from six yards in the 49th minute.
Dagenham came close to regaining the lead in the 63rd minute when Strevens volleyed an inviting Saunders cross wide of goal from six yards.
Roberts almost handed Barnet the lead in the 72nd minute when he fumbled a powerful strike from Jason Puncheon but recovered well to smother the danger.
The Bees almost snatched a late winner in stoppage time when Puncheon fired in a fizzing strike from the edge of the box which Roberts did well to palm to safety.