Barnet keeper Lee Harrison's howler gifted Accrington a point as they came from behind at Underhill.
Roscoe D'Sane almost gave Stanley the lead on 43 minutes, but fired against a post when one-on-one with Harrison.
After the break Ian Craney curled home a delightful free-kick before Liam Hatch scored a sensational solo effort.
Sagi Burton then put the home side in front after 69 minutes but Stanley levelled when Harrison spilt the ball, leaving D'Sane to steal a point.
Barnet: Harrison, Devera, O'Cearuill, Burton, Nicolau, Carew, Bishop, Wright, Puncheon, Hatch (Norville 90), Birchall (Grazioli 88).
Subs Not Used: Beckwith, Leary, Hendon.
Booked: Burton, Hatch.
Goals: Hatch 59, Burton 70.
Accrington Stanley: Dunbavin, Cavanagh, Roberts, Williams, Branch, Richardson (Miles 79), Proctor, Harris, Craney (Brown 74), D'Sane, Mullin.
Subs Not Used: Fearon, McGivern, Webb.
Booked: Williams.
Goals: Craney 51, D'Sane 83.
Att: 2,178.
Ref: Roger East (Wiltshire).
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