Paul Cox's men booked a trip to Ashton United this Saturday, as they took full advantage of Nuneaton being dramatically reduced to 10 men after just eight minutes.
Goalkeeper Tony Breedon was the man dusmissed following a challenge on Ben Stephens to hand the home side an early numerical advantage,
But the Poppies were shell-shocked on 22 minutes as they then fell 1-0 behind on 22 minutes with Joel Kettle on target.
Kyle Perry headed the home side level just two minutes before the break, which meant there was all to play for in the second half.
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And it was a 45 minutes that belonged to the Poppies.
They edged 2-1 ahead on 49 minutes when Decarrey Sheriff netted, and after the Poppies had squandered a string of chances, he scored his second to make it 3-1 after 58 minutes.
That knocked the stuffing out of Nuneaton, and the Poppies soon wrapped up their victory.
Sherriff completed his 17-minute treble on 66, before Ryan Fryatt made it 5-1 to complete a devastating four-goal salvo in the space of just 19 minutes..
Kettering then coasted to the final whistle ahead of their third round trip to Greater Manchester this weekend.
Ashton progressed thanks to a penalty shootout win over National League North York.
The two sides drew 3-3 before Ashton won the shootout 4-2.