The National League side had played out a 1-1 draw with Newport in the third round earlier this month, meaning that they would welcome the League Two team to the Silverlake Stadium for a spot in the fourth round.
But for Eastleigh the night got off to the worst possible start when Aaron Wildig gave the visitors the lead after just three minutes to silence a buoyant home crowd.
Paul McCallum pulled the non-league side back into the tie shortly after half time, however, it took just 12 minutes for James Clarke to make it 2-1 to Newport.
Eastleigh huffed and puffed to keep their fairytale run alive, but Will Evans put the tie to bed just 11 minutes from time.
Ultimately it just wasn't to be as Newport earned their spot in the next round.
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After being drawn at home to Manchester United in the fourth round, Eastleigh had been dreaming of welcoming Erik ten Hag's side to the 5,500 capacity ground in the next round.
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