Substitute Cavaghn Miley's 82nd minute goal meant Town fell to a fifth defeat of the season on their first visit to Silverlake Stadium.
Joe Leesley had fired Town ahead inside the opening two minutes with an emphatic finish, but Ben Williamson finished well to ensure the sides entered the interval level.
Town looked dangerous and capable of claiming a winner, but Eastleigh counter attacked quickly with just eight minutes to go with Miley striking the decisive blow.
Simon Weaver made two changes from last weekend's FA Trophy win over York City as Callum Howe and Lloyd Kerry came in for Kelvin Langmead and Jack Muldoon.
Town made a lightening quick start to the contest with Leesley blasting home within two minutes.
James Belshaw's free kick from deep inside his own half had run through to the winger who volleyed home on his left foot after Dom Knowles had battled with the Eastleigh centre half.
After playing his part in the opening goal, Belshaw was kept busy at the other end, claiming multiple crosses into his box, before Kerry forced a save from Max Stryjek with a 30 yard drive.
There was nothing Town's number one could do about Williamson's equaliser in the 27th minute though as a low cross from the right was directed first time into the bottom right corner.
Town had an excellent chance to restore their advantage eight minutes later as Ryan Fallowfield picked out Jack Emmett on the edge of the box, but the midfielder couldn't direct his left footed finish inside the post.
It was then the turn of the hosts to squander an opportunity as Joey Jones broke forward and found top scorer Paul McCallum at the far post, but the ball looked like it took a bobble before it was struck goalwards and ended up over the bar as a result.
The Spitfires created the last noteworthy chance of the half as a left sided corner found centre back Reda Johnson alone at the back post, only for the Eastleigh man to head wide.
Town again made a fast start to the half as Emmett tested Styrjek, though neither team were giving an inch, resulting in few chances.
Weaver introduced both Aaron Williams and Michael Woods in the hope of finding a winner, though it was Leesley who came close to finding the back of the net again as his corner, Town's first of the afternoon, bounced back off the cross bar and away.
Despite Town looking the more likely, substitute Miley was found on the counter attack and bent the ball past Belshaw to put his side ahead for the first time, in the 82nd minute.
Town piled men forward looking for an equaliser, including Mark Beck from the bench, though Thomson's attempt that looked destined to level the scores was blocked on the line, sending Town home empty handed.
Town: Belshaw, Fallowfield, Falkingham, Howe, Burrell, Thomson, Emmett (Beck 83), Knowles (Wiliams 73), Leesley, Kerry (Woods 69), Kitching
Subs not used: Cracknell, Muldoon
Goals: Leesley 2
Booked: Howe, Falkingham
Eastleigh: Stryjek, Hare, Green, Johnson, Boyce (Gobern 77), Wynter, Jones, Hollands, Yeates (McKnight 90), Williamson (Miley 77), McCallum
Subs not used: Zebroski, Dennett
Goals: Williamson 27, Miley 82
Referee: W Finnie