Albion have been drawn at home to League Two newcomers Newport County in the first round of the Capital One Cup.
The tie takes place at The Amex in the week commencing August 5 and will be the Seagulls' first home game of the season after an away start in the Championship on August 3 to avoid a clash with the Pride festival.
Newport are back in the Football League following a 25-year absence. They defeated fellow Welshmen Wrexham in last month's Conference play-off final at Wembley with two late goals.
County are managed by former Tottenham defender Justin Edinburgh. He was in charge of Rushden and Diamonds when they were knocked out of the FA Cup by Albion at Withdean in 2009.
Crawley have been drawn away to Cheltenham.
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