Ben Strevens scored the last minute winner in the first round win against Lincoln City
Eastleigh will play either League Two Dagenham & Redbridge or Vanarama Conference rivals Southport in the FA Cup second round.
The Spitfires got to this stage of the oldest cup competition for the first time in their history after beating Kidderminster in the fourth qualifying round.
Richard Hill's side then beat Lincoln City 2-1 on Saturday in the first round thanks to a Ben Strevens last minute goal.
They are now just one round away from facing possible Premier League opposition. They must wait to find out their next opposition with Dagenham and Southport due to play a replay on 18 November.
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