Simon Weaver’s side found themselves trailing early on in Saturday’s clash but recovered to seize a 3-1 lead, only to end up hanging on after gifting their visitors a second of the afternoon.
The hosts began sloppily, misplacing a number of passes and just six minutes were on the clock when they fell behind.
Josh Huggins held off Warren Burrell down the Havant right and nodded infield where the unmarked Nicke Kabamba picked up the ball in space.
The Hawks’ powerful centre-forward drove left to right towards the Town box and then fired a strike back across James Belshaw and into the bottom corner of the net.
The Harrogate response was however fairly swift and they were back on terms a little over five minutes later.
Joe Leesley’s corner from the right was cleared, but Liam Agnew sent the ball straight back to the winger who curled a delightful cross into the box where Callum Howe rose highest and powered home a header.
Town settled into something of a rhythm after drawing level, though it was the visitors who went closest to grabbing the next goal as the ball found its way into the path of Kabamba, the lively frontman breaking at pace before dragging an effort just wide of Belshaw’s far post.
Weaver’s men did go on to finish the opening period on the front foot and Knowles slotted a Muldoon pass past Ryan Young, only to be denied by an offside flag, which meant half ended all-square.
Dominic Knowles curled a strike just too high shortly after the resumption, but then found his range to put Town in front in the 52nd minute.
George Thomson’s corner from the right sparked a scramble in the Havant six-yard box and the ball eventually fell for the Harrogate marksman to force home at the back post just a couple of yards out.
The game then appeared to be all but over five minutes later when Town added a third.
Knowles danced past a Havant defender and into the box before pulling back from the right towards the penalty spot where the waiting Jack Muldoon squeezed a shot through Young.
The home side seemed to be cruising to another three points, only to hand the Hawks a route back into the contest.
Lloyd Kerry lost possession inside his own box and the ball broke for Kabamba to lift delicately over the dive of the sprawling Belshaw.
That gift visibly lifted Havant, the Hampshire outfit enjoying a decent spell of pressure as they sought an equaliser, however the Town defence held firm for a third win on the spin, extending their unbeaten run into a 10th game.