A stoppage time winner from Shaquille Coulthirst gave the Bees all three points in an entertaining game in Hampshire.
A first half strike from Jack Taylor was cancelled out by Jack McKnight's second half leveller.
But the drama was far from over as Coulthirst netted deep into added time to send the travelling Bee army into raptures.
The Bees started on the front foot and put together a nice move in the opening five minutes. However, J Taylor's cross was just over the head of Akinola.
On 11 minutes Max Stryjek was forced into his first save of the afternoon, Mason-Clark set it back for Callum Reynolds, but the skippers strike was palmed wide by the Eastleigh keeper.
After 16 minutes the Bees took the lead through Jack Taylor as he superbly bent the ball into the top left corner, it was a superb strike from the 21 year old.
Eight minutes later it was almost two for Darren Currie's side as Simeon Akinola launched a shot for the top corner from the edge of the box, but the attackers effort went a couple of yards wide of the far post.
13 minutes before the break, Akinola was involved again as he rose highest from Sparkes free kick, but he didn't make the contact he would have wanted and the Spitfires cleared.
At the other end Jack Mcknight dragged an effort wide after Barnet failed to clear their lines, it was a let off for the Bees after they dominated large stages of the opening 45 minutes.
On 41 minutes Scott Loach was called into action as Williamson struck from a well worked corner, but the Bees number 1 flew across his goal and diverted the ball away.
At the start of the second half, a superb block from Harry Taylor denied the hosts the leveller as the midfielder threw himself at Barnett's powerful drive.
Barnet had two golden chances on the hour mark, firstly Akinola did well to create space to meet J Taylor's cross but his header was straight at Stryjek. A minute later the Eastleigh keeper made a superb stop at point blank range as Josh Walker wriggled away from the defence and fired at goal.
On 67 minutes there was controversy as Walker was brought down by the already booked Johnson, however referee Lee Collins decided that the striker had dived as he raced clear on goal.
With 20 minutes to play the Bees were pegged back as the ball broke to McKnight six yards out and he coverted past Loach to level the scores.
Dan Sparkes nearly put his side back infront as he curled a brilliant free-kick just wide of the post from 25-yards-out.
With five minutes to go the hosts were reduced to 10 men as Smart was shown a second booking for simulation as he went down too easily in the eyes of the referee.
With time running out there was a chance for Akinola as he burst through on goal but his lofted effort went over the bar as lifted it over the onrushing keeper.
Into added time and J Taylor forced Stryjek into another stop as he tried his luck from 30 yards out, but the Sptfires keeper was equal to the Irishmen's effort.
The Bees found the winner in the fourth minute of added on time as substitute Shaquile Coulthirst tapped home from Sparkes' cross after Stryjek dropped a long ball into the area.
The Bees now have a short break until their next game as they take on Maidenhead at The Hive, where they will look to buld on the first month of the season where they have lost just once.