Barnet had both Liam Hatch and Barry Cogan red-carded by referee Dean Whitestone in a controversial second half and Accrington exploited their numerical advantage to scoop maximum points.
After an uninspiring opening 40 minutes, Accrington took the lead when Barnet skipper Ian Hendon was judged to have fouled Robbie Williams inside the area and Whitestone pointed to the spot.
Midfielder Andy Todd assumed responsibility for the ensuing spot-kick and he lashed his effort past Barnet keeper Rob Burch.
But Barnet responded on the stroke of half-time when the home side's brand of high-tempo passing led to Adam Birchall sweeping in Cogan's cross from close range.
After the break, Barnet cranked up the pressure and Accrington keeper Przemyslaw Kazimierczak, on loan from Bolton, was forced to produce two fine saves to keep the home team at bay.
Both Andy Hessenthaler and Birchall came agonisingly close to putting Barnet in front, but Accrington weathered the storm, and refused to buckle.
Nevertheless Barnet still seemed to be on course for three points until substitute Hatch was sent off for allegedly aiming an elbow at Accrington defender Mauro Almeida.
Hatch looked stunned as he marched off the pitch and the decision enraged an already volatile Underhill crowd after Whitestone had waved away two clear-cut penalty appeals for Barnet.
Cogan was then given his marching orders for a second yellow card after a foul in stoppage time to compound a thoroughly miserable afternoon for Paul Fairclough's side.
Prior to the club's record-breaking FA Cup run, Barnet were hovering on the fringes of the play-off race, but recent results suggest that the Hertfordshire club will be forced to settle for mid-table mediocrity this time around.