Wes Thomas opened the scoring for AFC Bournemouth with a well-taken finish early on in a first-half which the Cherries had most of the ball.
But the Hawks sprung into life after the break and equalised through substitute Kabba, and nearly went ahead minutes later through Ryan Wignall.
Kabba then set up Ollie Palmer to take the lead for the hosts, before Kabba forced a vital third goal – though it did take a cruel deflection.
In a quiet opening to the game, Lewis Grabban had the only attempt on goal with a free-kick skied over the bar. The Cherries bossed possession though, and took the lead after fifteen minutes through Thomas.
Bournemouth legend Steve Fletcher took a knock moments before the opener, and made way for Alex Moth has the players repositioned after the goal.
Young defender Baily Cargill picked out Thomas with an excellent aerial through-ball, and the ex-Crawley striker controlled it well and coolly finished past Hawks’ goalkeeper Clark Masters.
Ten minutes later, an efficient breakaway move resulted in a chance for Grabban, who cut inside well, but his fierce effort was just wide of the goal.
Thomas nearly bagged his second of the game with an impressive turn and shot, but Havant ‘keeper Masters was equal to the strong shot.
Substitute Moth was denied by Masters in a one-on-one, before Hawks’ trialist Steffan Bailey fired just over the bar on the stroke of half-time.
Paul Groves made three changes at the break, with Simon Francis, Miles Addison and Thomas making way for Ryan Case, Dan Strugnell and Harrison Gilkes.
Havant stepped up their game after the break, and the energetic Wignall went close after a good team move.
A number of development players were then introduced, giving a fresh look to the Cherries side for the last 30 minutes.
The hosts equalised just after the hour mark when substitute Kabba burst into life, cutting inside from the left and hammered past Darryl Flahavan.
Palmer nearly completed a rapid turnaround for the Hawks, but his shot came off the post – a let off for the Cherries.
That prompted a response from Paul Groves’ men, and they nearly retook the lead when Harrison Gilkes came close at the back-post after some good work from Moth down the right.
But the hosts took the lead after 70 minutes. Kabba turned provider this time, causing problems down the right and finding Palmer, who slotted home to take the lead.
And the two combined again ten minutes later, and Kabba’s strike took a wicked deflection off Cargill, and rolled past Flahavan for the third.
Steve Ramsey came close for the Hawks late on with a curling free-kick, but 3-1 was how it stayed.
Havant: Masters (Pegler, 45), Hinshelwood, Arthur, Hutchinson, Pearce, Harris, Wignall, Bailey, Moss, Palmer, Taggart. Subs: Stockford, Ramsey, Jones, Moss, Ryan, Hopkinson, Ramsey, Kabba, Woodford, Whyte, Newton, Pegler.
Goals: Kabba (62, 81) Palmer (70)
Cherries: Flahavan, Francis (Strugnell, 45), Cook, Addison (Case, 45), Meade, McDonald (Stockley 60), Wakefield, Gregory (Makoni 60), Grabban (Jamal 60), Fletcher (Moth, 15), Thomas (Gilkes, 45).
Subs: Gilkes, Moth, Tierney, Strugnell, Cargill, Makoni, Case, Stockley.
Goal: Thomas (15)