The Bees best chances came via Keanu Marsh-Brown and Harry Crawford with the latter heading over from eight-yards early in the second-half.
Woking had three golden opportunities in the dying stages of the contest but they were denied by a resolute Bees’ defence and Graham Stack and Iffy Allen on the line.
The first chances of the match came from range with Kevin Betsy and Curtis Weston both shooting wide.
Gavin Williams was next to try his luck but Stack was alert to divert his powerful strike around the post for a corner.
The home side continued to push with Josh Payne volleying just over before Jack Saville did excellently to divert John Goodward’s goal-bound strike away from goal.
The Bees showed flashes of what they can do with their best chance before the break coming when Marsh-Brown burst past the Woking midfield and shot just wide.
After the restart Edgar Davids’ side had a golden opportunity to take the lead but Crawford headed wide from close-range after good work from Marsh-Brown.
Youngster Iffy Allen was introduced midway through the half and he immediately added something new to the Barnet attack.
The impressive forward first showed his stunning ability when jinxed past three Woking defenders before cutting the ball back where Keiron Cadogan and Marsh-Brown had shots blocked on route to goal.
Luisma Villa was also introduced which allowed Marsh-Brown to move into a free role. The move almost paid off as the Bees’ top scorer raced through on goal and finished only to turn and see the linesman’s flag raised for offside.
During the final stages the home side regrouped and they had more than one chance to take all three points.
McNerney was first to try his luck but Stack produced a instinctive save with his foot before Jack Parkinson headed over from the resulting corner.
Just moments later McNerney was in the thick of it again when he headed over Stack and seemingly into the net until Allen came from nowhere to clear the ball off the line.
Anthony Acheampong saw a header saved late on but the match ended 0-0 with Barnet securing their first clean sheet since August.