Watched by a crowd of 943, a 47th minute goal from Gareth Dean was enough to see Kevin Wilkin's side through.
In the Red Insurance Southern League Cup, Leamington needed a penalties victory to win at Evesham United. The game finished 0-0 after extra time and The Brakes won 3-1 on penalties in front of a crowd of 112.
Bedworth United are also through thanks to a 3-1 win against Stourport Swifts. Connelly put the visitors ahead but Bedworth hit back with goals from Withers (28) and Ramsey (33) before Withers hit the third of the night with four minutes remaining.
Rugby Town are the third Warwickshire side through thanks to a 3-1 away win at Halesowen Town. A hat-trick from Keene (25,37 & 78 pen), cancelled out a 41st minute goal from Gater.
Atherstone Town lost 1-0 at home to Cinderford Town with O'Connor scoring the only goal of the game in the 37th minute.
Stratford Town are through in the Polymac League Cup after beating Coleshill Town 2-1 at home in the first round. Nathan Edgington scored the goals for Jason Cadden's side who now travel to Coventry Sphinx in the second round.