Shane Byrne’s penalty was the difference between the teams as Brackley found a way past impressive Eastleigh goalkeeper Nick Townsend in a 1-0 win.
Matt Lowe’s drive after a flowing move was saved at the second attempt by Townsend and Morgan Roberts curled a free-kick just wide.
Lowe was denied again before Byrne’s spot-kick gave the hosts a half-time lead, thanks to Cameron Gregory then saving Aaron Blair’s lob.
Town went close to a second through Zak Brown’s curler and Kyle Morrison’s header, with Townsend spreading himself well to again save from Lowe and then tipping over Roberts’ late drive.
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