Swift response from Saints
Manager Luke Fogarty made a number of changes, with Alex Shaw replacing the injured Quentin Townsend in defence and former Massey Ferguson midfielder Mark Anderson making his debut.
Saints were soon on the back foot with Simeon Smith testing home keeper James Stott.
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Hide AdRoss Jackson then beat two defenders, before shooting wide, with the unmarked Luke Church looking a better option.
Southam took the lead when James Hardie shots was helped into his net by off-balance Bolehall keeper Ian Kimberley.
This was the signal for the visitors to pick up their pace, mainly through Brakes wide man Grant Roscorla, who went head-to-head with Jack Taylor in an absorbing contest.
But, it was Southam who increased their lead in the 38th minute. A John Blunsom free-kick eventually fell to Jackson on the edge of the box and he cleverly rounded Kimberley to tuck the ball home despite the desperate efforts of Lee Millard.
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Hide AdBolehall scored the best goal of the afternoon four minutes after the break, with defender James Abbott finding the net with a immaculately placed shot following a swift exchange of passes.
Swifts piled on the pressure with Stott needing to be at his best to deal with a goalbound flick from Smith.
However, Saints held out to reach the third round where they will visitFairfield Villa or Walsall Wood.
Southam’s Birmingham County FA Midweek Floodlit Cup tie with Racing Club Warwick was called off two hours before kick-off on Tuesday night due to a waterlogged pitch.
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Hide AdFollowing the Swifts win, the Swifts left Fogarty a fustrated man.
He said: “ In view of the conditions, the referee had no option, but the lads were keen to play and build on Saturday’s result.
“We blooded some younger players against what was a very strong Bolehall side and I was pleased with the team’s performance.
“Luke Church and Alex Shaw have been waiting patiently for their chance and both came up trumps.”