Barnet had the first chance of the game, Byron Harrison chesting the ball down to Charlee Adams but his half volley went over the crossbar.
Medy Elito powered at goal in the 13th minute but his shot from 25 yards out didn’t trouble former Bee Graham Stack in the Eastleigh goal.
The visitors took the lead as the clock ticked into the 20th minute, the ball falling as far as Michael Green who rifled a shot high into the top right corner from the edge of the box, giving Mark Cousins no chance.
Jack Taylor shot over the crossbar while at the other end Oscar Gobern looped the ball into the Terrace behind Cousins’ goal.
Stack was quick off of his line to stop Shaq Coulthirst as he raced down on goal before the Eastleigh number 1 was called into action again, excellently palming Sparkes’ powerful shot over the bar.
After the break, Paul McCallum hit the side netting but would have more luck in the 64th minute when he doubled Eastleigh’s advantage.
A free kick close to the byline was whipped in towards the far post where McCallum rose highest to head home.
Cheye Alexander was the next to see an effort saved by Stack.
Barnet pulled a goal back on the stroke of 90 minutes. Charlee Adams firing home for the edge of the box.
Barnet – Cousins, Alexander, Johnson, Robson (c), Adams, Harrison, Coulthirst, Sparkes (Walker, 67), J. Taylor, Elito (Mason-Clark, 59), Sweeney.
Unused – Matrevics, Fonguck, Tutonda.
Attendance – 1,028 (86 Eastleigh)
Referee – Danny Middleton