A Duku double and a Walker chip seal all three points for the Bees in Hartlepool.
It was the hosts who started stronger and had the first chance of the game, Paddy McLaughlin trying to angle the ball goalwards but Dan Sweeney was there to block his effort.
Hartlepool took the lead with 9 minutes on the clock. A cross came in and Mark Cousins missed his attempted punch. This allowed McLaughlin to shoot at goal but it was turned in by defender Peter Kioso who could make no mistake from very close range.
Minutes later Kioso had a chance to double his and Hartlepool's tally, but his header from Liam Noble's free-kick was off target.
Kenton Richardson was the latest to have a go at Cousins' goal, but his drive from 25 yards out went narrowly the wrong side of the post.
The Bees first chance came midway through the first half, could work from Manny Duku saw him supply Jack Taylor only for the midfielders half volley to strike the side netting.
Sweeney was again cancelling out efforts at the back, this time getting a crucial challenge in to deny Luke James' strike.
Barnet's equaliser came in the 24th minute. Cheye Alexander set up Sweeney who delivered a great cross from the right and Duku rose highest to powerfully head home.
Just 53 seconds later, Barnet were in the lead. From the kickoff, Duku applied pressure forcing Kioso into an error. The Dutch forward raced down on goal and coolly lofted the ball over the top of Scott Loach.
Duku, now on a hat-trick, would be stretchered off shortly before the break and replaced by Byron Harrison.
After the restart, the Bees continued to put pressure on the Hartlepool goal. Taylor had an effort deflected wide and from the following corner, Elliott Johnson inswinger had to be dealt with at the near post by Loach.
Charlee Adams lined up a shot from range which whistled just over the crossbar before Harrison was set through one-on-one at a tight angle and his dink over Loach went agonisingly the wrong side of the post.
With only a one-goal advantage, there was always a chance for Hartlepool to get back into the game and Taylor was called into defensive action when we expertly headed the ball off the line.
With the clock ticking down, Barnet needed that two-goal cushion and substitute Josh Walker was given an excellent opportunity to get it when he was set through by Harrison. However, under pressure from two Hartlepool defenders, his chip went over the bar.
James' had an effort blocked by Sweeney at one end before Alexander stung the hands of Loach at the other.
Captain Callum Reynolds headed Nobles effort wide of target and Craig Robson had a header at the other end saved by Loach.
Into five minutes of stoppage time we went and the Bees found that elusive third goal.
A slip from Myles Anderson set Walker clean through on goal and he chipped the ball over Loach and into the back of the net, sending the 47 Barnet fans that had made the long trip home happy.
Barnet: Cousins, Alexander, Johnson, Reynolds, Robson, Adams, Taylor, Fonguck, Sweeney, Duku (Harrison 45), Bettamer (Walker 69).
Subs Not Used: Sparkes, Matrevics, Elito.