Scott Doe scored his second goal of the season just after half time to give the Wood the lead at the Amlin Stadium.
Six minutes later, Luke Howell's curled effort from distance ensured the visitors took all three points.
The hosts misery was doubled late on as defender Matt Paine was sent off for two bookable offences.
Boreham Wood's shock victory over promotion hopefuls Braintree Town saw them climb out of the National League relegation zone.