Lewis Hawkins scored his first AND second Hartlepool United goals.to inspire Pools to a vital away win.
The midfielder smashed in two stunners in the 34th and 40th minutes at the Hive after Fumnaya had put the Bees ahead with an 11th-minute beauty of his own.
Nathan Thomas scored his first goal for Pools in the 62nd minute to send the 336 away fans into ecstasy.
Pools began well with Carroll and Gray combining well, finding Thomas, who cut off the right wing and curled his left-foot shot just wide of Stephens' top corner.
But Barnet went in front with a stunning 11th-minute strike from SHOMOTUN.
The young midfielder came in off the right side and shot left-footed into Trevor Carson's top right corner.
Pools had a great chance to level through Luke James who was put through by Thomas, but the forward hit hois shot straight at Stephens who saved with his legs.
However, Pools equalised in the 34th minute and when it came it was a wondergoal from HAWKINS.
The midfielder was afforded time and room 30 yards out and he indulged, smashing his right-foot shot into the keeper's bottom right corner.
Gray just then just wide at far post after a teasing Thomas cross from the left.
But Pools were not to be denied and it was HAWKINS again, with Billy Paynter setting him up.
This time Hawkins was 'only' 20 yards out, the keeper getting his hand to it but could not keep it out of his left corner.
Pools started the second half in fine fettle.
And they were 3-1 up in the 62nd minute and it was another beauty.
THOMAS was the marksman, letting fly with a left-foot shot from the ede of the box into the keeper's right corner.
James tried his luck in the 66th minute but his shot ballooned off a defensder for a corner.
Jones tried to get Paynter away with long ball in the 71st minute but keeper Stephens came out well.
Pools continued to have the better of play, moving the ball around nicely.
Paynter threw a tizzy eight minutes frim time after being penalised for a handball when looking to break through.
HIgnett made three changes in the latter stages, bringing on Michael Woods, Rhys Oates and Brad Walker.
Barnet: Stephens, Yiadom, N'Gala, Nelson, Johnson, Shomotun, Togwell (Gambin 61), Randall (Muggleton 54), Weston, Roberts (Stevens 54), Akinde
Unused subs: McKenzie-Lyle, Champion, Sesay, Pearson
Booked: Nelson 69, Muggleton 83
Goal: Shomotun 11
Pools: Carson, Magnay, R Jones, Bates, Carroll, Featherstone, Hawkins (Walker 87), Gray (Woods 75), Thomas (Oates 78), Paynter, James.
Unused subs: Bartlett, Richards, D Jones, Fenwick
Goals: Hawkins 34, 40; Thomas 62
Booked: Magnay 80
Referee: Darren Handley
Att: 1,734 (away 336)