Younes Kaboul, Paris Cowan-Hall and Danijel Subotic were also on target for Paul Hart’s side as they bagged a big victory at the Silverlake Stadium.
French defender Kaboul gave Pompey the lead after five minutes when he headed home Angelos Basinas’ cross and Cowan-Hall quickly doubled the Premier League side’s advantage as he turned home an effort from close-range.
Eastleigh handed Portsmouth their third goal when Tom Jordan’s back-pass raced away from goalkeeper Jason Matthews to leave Subotic with a simple chance.
Brett Williams pulled a goal back for the hosts just before the break but Pompey were able to extend their advantage in the second 45 minutes.
Nugent bagged his first goal with a neat finish from Eugen Bopp’s pass and he continued his impressive outing with a powerful volley and a calm lob to secure a hat-trick for himself and a 6-1 win for the Fratton Park outfit.