The Quakers – who have now not won in seven attempts at Underhill – failed to find top form but wayward home finishing meant they claimed the point that sent them above Hereford into third.
Top-scorer Tommy Wright squandered a 10th-minute chance when he shot wide from five yards after good work by Julian Joachim.
Barnet, on the back of three successive home wins, came closest to breaking the deadlock in the first-half with impressive winger Albert Adomah firing wide after 19 minutes.
Six minutes later, Kieron St Aimie’s overhead kick flew over with Rob Purdie also flashing a shot wide at the other end.
Twelve minutes from time, substitute Cliff Akurang failed to convert Adam Birchall’s cross.