Ashley Barnes finished well to give the hosts the lead on 18 minutes, which they held comfortably until the 67th minute when Inigo Calderon was sent off after a strong challenge on Byron Anthony.
The challenge saw the defender stretchered off with a serious ankle injury, but the League Two side pushed hard thereafter and were rewarded in the 81st minute, when substitute Danny Crow bundled the ball in to force the tie into extra time. Crow grabbed his second before Conor Washington completed a 3-1 victory at the Amex Stadium.
Birmingham City also struggled against Plymouth Argyle at St Andrews, with Lewis Alessandra scoring late to force extra time. However, Kyle Bartley scored two minutes into the allotted 30 to seal the Blues' progression.
Cheltenham had to come from behind twice at home to Crawley Town. A Matt Richards penalty had cancelled out Gary Alexander's opener, before two Nicky Adams strikes put the visitors two up. The hosts came back again though, through Terry Gornell and Bryon Harrison, to take the match into extra time. Harrison's second of the night guaranteed their progress into the second round.
Brighton 3-1 Newport, Barnsley (5)0-0(4) Scunthorpe, Birmingham 3-2 Plymouth Argyle, Cheltenham 4-3