James Dance scored twice as Kettering came from behind to end Newport's unbeaten home league run, which stretched back to March 2009.
Charlie Henry put the hosts ahead early on with a shot from outside the area before Dance levelled with a close-range header after being left unmarked.
Kettering were reduced to 10 men after the break when Greg Taylor was sent off for a foul on Kerry Morgan.
But Dance then headed in a second after again being left free in the area.
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