Albion have been drawn away to League 2 Newport County in the third round of the Emirates FA Cup.
Newport are currently top of League 2 and have developed a giant-killing reputation in recent years, holding Tottenham to a draw in 2018 before losing the replay and knocking out Premier League Leicester City with a 2-1 win at Rodney Parade two seasons ago.
The clubs have met three times in the FA Cup, most recently in 1966 when Albion won 2-1.
Albion beat Newport 8-1 in 1955 at the Goldstone but Newport won the first FA Cup game between the sides, 3-1 in 1948.
Third round ties will take place over the weekend of January 9-10.