The first chance of the game fell to Barnet 11 minutes in, a free kick found Payne at the far post but he couldn’t get a shot away.
In the 21st minute, Alex Nicholls saw his shot from 20 yards out trickle past Smith’s right hand post.
Shortly after, McKenzie-Lyle was forced into a great save to his right to deny a stinging half-volley from Woodards.
Boreham Wood broke the deadlock in the 37th minute, Shaun Jeffers curling a shot past the helpless McKenzie-Lyle.
After the break, Dan Sweeney headed a cross down to the feet of Shane Cojocarel, but his shot was saved.
Boreham Wood doubled their lead 10 minutes after the restart, Tom Day conceded a penalty and up stepped Jeffers who sent McKenzie-Lyle the wrong way.
Barnet hit back straight away, Nana Kyei picking up on some loose defending before slotting home.
In the 79th minute, Boreham Wood revived their two goal cushion, an effort from distance was violently deflected sending McKenzie-Lyle the wrong way, the ball struck the post before Balanta ran in to head home.
With almost the final kick of the game, it was four. Clever play by Smith undone the Barnet back line, he pulled it back and Murtagh placed it home.
Barnet XI – K McKenzie-Lyle, Day, Hernandez, Sweeney, Smith, Payne (c), Trialist, Coker, Nicholls, Cojocarel, Kyei. Subs – R McKenzie-Lyle, Connell, Sylla, Adina, Aghadiuno, Annesley.