A second half fight-back saw Barnet run out victors in a pulsating match at The Hive.
Fraser Franks’ opened the scoring after 11 minutes, heading a Steven Schumacher corner past Bees’ debutant Max Crocombe.
Bondz N’Gala levelled things up for Barnet, firing into the Stevenage net after a Curtis Weston knockdown on 48 minutes.
Stevenage restored their lead barely two minutes later – Hitchcock headed past Crocombe following a Schumacher free kick into box.
The Bees levelled after 62 minutes when Aaron McLean powered a John Akinde cross past Jesse Joronen in the Stevenage goal.
Barnet seized the lead in the 78th minute after Michael Gash slotted home an Akinde cross from the left.
The Bees’ best chance of the opening period had fallen to midfielder Curtis Weston.
On 26 minutes Weston received a through ball on the edge of the box, but his low shot on goal was palmed away by the ‘Boro keeper.
In a first half short of chances, Sam Togwell fired a shot over the bar from distance after 36 minutes.
The game to life following the break.
Just after the re-start Chris Whelpdale headed just wide of his own goal from a Barnet corner.
On 57 minutes McLean struck a shot high over the bar, following a left sided cross into the box.
A Gambin run and pass was fired agonisingly over the bar by Akinde with 65 minutes on the clock.
The Bees were in the ascendancy and it was Akinde who again put the ball over, following a good pass across the box by Gash.
Dembele’s header was then tipped over the bar by Joronen on 81 minutes, after Gash’s high cross from the right.
A low injury time drive by Boro’s Dipo Akinyemi was the visitors’ best chance of the second half.
But the Bees held on to claim all three points, and will be in buoyant mood when Dagenham & Redbridge visit the Hive next weekend.
Barnet: Crocombe, Hoyte, Johnson, Dembele, N’Gala, Yiadom, Weston, Togwell (Gash 56’), Vilhete (Gambin 53’), McLean, Akinde (Nelson 88’).
Subs not used: McKenzie-Lyle, Muggleton, Shomotun, Stevens.