Alex Nicholls opened the scoring for the Bees in the first half, but Billy Kee' penalty means both sides share a point at The Hive London.
Barnet started well and they were rewarded for their efforts with a goal 18 minutes in. John Akinde brought the ball down before finding Vilhete who, rather than shooting, found Alex Nicholls who stroked home past Chapman.
Chapman was called into action when Ricardo Santos' powerful header from Ryan Watson's corner was caught well by the Stanley 'keeper.
Brindley had a chance from a free kick, but his attempt went narrowly over the crossbar and the Bees had a 1-0 advantage at the break.
Accrington came back out on the front foot, Liam Nolan had an effort saved before Craig Ross again denied the visitors, Jordan Clark failing to get past the Barnet goalkeeper.
Stanley's best opportunity of the first half fell to Jordan Clark, who fired disappointingly wide from inside the box.
Referee Brett Huxtable then awarded Accrington a penalty after Dan Sweeney was adjudged to have fouled Jimmy Dunne. Sky Bet League Two's top goalscorer Billy Kee stepped up and made no mistake.
However, Barnet would rally in the final 15 minutes. John Akinde broke free of his marker but fires at Chapman and Jack Taylor would shot over the crossbar.
Ross' free-kick from inside his own half would find the head of Dan Sweeney, but the ball went wide of the target.
Substitute Jordan Nicholson found a yard of space but fired straight into the gloves of Chapman.
The Bees best chance came when John Akinde headed what must have been an inch wide of the right-hand post.
Akinola saw an effort tipped around the post and at the other end, Nolan dragged a shot wide.
In stoppage time, Barnet had claims for a penalty waved away as Chapman clattered Akinde in the penalty area, but the referee awarded a drop ball.
The Bees remain unbeaten at home under Graham Westley's stewardship.
Barnet: Ross, Brindley (Clough '68), Santos, Watson, Weston, Akinde, J. Taylor (Nicholson '80), Tutonda, Vilhete (Akinola '50), Nicholls, Sweeney.
Unused: Legg, Coulthirst, Sule, Plavotic
Attendance: 1501 (185 Accrington)
Big Amber Draw: 05929