But north London neighbours Wealdstone fell to defeat by the same margin in Gateshead after letting a lead slip.
Barely a minute was on the clock when Bees fell behind as Danny Whitehead gave Fylde a shock lead.
Marvin Armstrong sent an effort from the edge of the box wide as Bees looked to respond, with a good cross evading the head of captain Harry Pritchard.
Danny Collinge saw his shot deflected behind on 20 minutes and Zak Brunt lifted another attempt over the target just past the half-hour mark.
Laurie Walker made a good low save to deny Fylde a second on 34 minutes, before Anthony Hartigan’s free-kick was well saved at the other end.
And Collinge saw another shot sail wide of the far post after cutting inside shortly before half-time as Barnet’s frustrations grew.
Dean Brennan made a couple of changes around the hour mark, with Fylde reduced to 10 men when Siyabonga Ligendza was dismissed for a second bookable offence on 71 minutes.
And Pritchard had Barnet’s best chance of the game saved by the visiting keeper moments later, before Stead steered a low shot into the bottom corner to level on 80 minutes.
Bees were inches away from taking the lead in the third minute of injury time when Kabamba shot against a post.
But they got their reward in the dying seconds as Kabamba found the net.
Barnet: Walker, Hall-Johnson, Collinge, Armstrong (Stead 58), Kabamba, Kanu, Pritchard, Hartigan, Oluwo (Okimo 60), Potter (Barratt 83), Brunt. Unused subs: Gillmore, Senior.
Gateshead 2 Wealdstone 1
Wealdstone’s Sean Adarka poked wide after some neat footwork in the box on nine minutes, before Micah Obiero had a shot deflected wide after a strong run.
Jaydn Mundle-Smith flicked a header wide from the subsequent corner, before Jed Ward was called into action to tip an effort from Greg Olley wide and denying the home captain again soon after.
Marcus Dinanga also saw a pair of headers tipped over by Ward, who also kept out Olley again on 32 minutes and then thwarted Connor McBride from close range.
The hosts kept the pressure on and saw Dinanga head over from a late corner, but Stones went close soon after the restart as Alex Dyer had a low effort parried by Archie Mair.
Dyer was then booked for thwarting a counter-attack, before McBride fired wide from 10 yards and Dinanga shot over after latching onto a long ball.
Obiero glanced a low cross from Tarryn Allarakhia wide on 54 minutes, but Stones made the breakthrough when the roles were reversed and Obiero burst forward to tee up Allarakhia to slot into the bottom corner on 73 minutes.
Kyle Smith’s cross was met by Tahvon Campbell, but smothered by Mair moments later, before the hosts levelled as Olley teed up McBride to fire past Ward.
Allarakhia fired over from 25 yards, before Stones fell behind on 80 minutes as McBride found the net from fully 30 yards.
And only a brilliant save from Ward denied Dinanga a third goal in the sixth minute of stoppage time, as Stones made the long journey back to London empty-handed.
Wealdstone: Ward, Barker, Dyer, Marrett, Allarakhia, Obiero (Abdulmalik 87), Smith, Clayden, Bowen (Ferguson 87), Mundle-Smith, Adarkwa (Campbell 66). Unused subs: Cook, Andrews.
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