Shaq Coulthirst had the first chance of the game, dragging his effort wide of the target from 25 yards out.
Charlee Adams volleyed at goal after controlling with his chest forcing Elliott Justham into a good save.
Dagenham’s first chance came through an Angelo Balanta header which Mark Cousins was equal to.
The deadlock was broken in the 34th minute when a Medy Elito corner was headed goalwards by Callum Reynolds and poked home by Coulthirst from close range.
Soon after, Coulthirst forced a save from Justham soon after before Jack Taylor also tested the Dagenham number 1.
Balanta managed to wriggle his way through the Barnet defence and into a shooting position but Cousins was out quickly to deny him.
After the break, the Bees weathered an early Daggers storm through chances from Balanta and Wilkinson.
Simeon Akinola came off the bench for his first appearance of the season and provided an instant lift amongst the Barnet supporters.
Taylor and Sweeney both provided good deliveries which the Dagenham defence had to deal with well before Akinola curled one just over the bar.
Coulthirst was set racing down on goal but a good recovery from Clark denied the Barnet front man.
Taylor was set up by Elito and forced Justham into a good low save to his right with his effort.
Mullings had a golden opportunity to equalise with 10 minutes to play but headed over from 6 yards out unmarked.
The Bees saw the came out and picked up all three points.
Attendance – 1,775 (301 Barnet fans)
Barnet – Cousins, Alexander, Johnson, Reynolds, Robson, Adams, Coulthirst (Tutonda 86), J. Taylor, Elito (Harrison 76), Sweeney, Mason-Clark (Akinola 58)
Unused – Matrevics, Fonguck