Darlington striker Adam Marsh scored his first goal in senior football to secure a place for Quakers in the last 16 of the LDV Vans Trophy last night.
Marsh, signed from Worksop in November, struck in the second half just as Shrewsbury threatened to equalise and take the game into extra time.
Craig Liddle gave Gary Bennett's side an early lead in a competent performance by Quakers considering the tricky conditions and they now look forward to a game at either Port Vale or Chester in the area quarter-finals.
On a frozen pitch which passed an inspection just an hour before kickoff, Quakers took the lead after just four minutes.
Stuart Elliott picked out Liddle from a right-wing free kick and the defender confidently headed past Paul Edwards for his fifth goal of the season. But in the early stages it was obvious that both sets of players were having trouble keeping their balance.
Shrewsbury had a chance to equalise after 17 minutes when Darlington keeper Frank Van Der Geest, in for Andy Collett, punched away a cross only for Jamie Tolley to head the ball back to the box where Ryan Lowe, with his back to goal, failed to turn the ball in.
Quakers responded with a Phil Brumwell cross which David McMahon headed straight at Edwards, then Elliott ended a flowing move with a volley just over the top from 25 yards. Quakers should have gone further ahead after 29 minutes when McMahon found Paul Heckingbottom overlapping on the left and the striker ran into the middle where he headed the return cross from the full back wide from six yards.
Quakers kept up the pressure and the outstanding Hodgson put a teasing cross into the six-yard box which defender Ross Davidson glanced out for a corner in front of the on-rushing Paul Campbell.
Experienced striker Nigel Jemson was lucky to escape censure just before half-time when he appeared to slap Hodgson, before the former Nottingham Forest youngster curled a free kick from the corner of the box just wide of the post.The second half started with a yellow card for Hodgson who went down when challenged by two defenders as he dribbled into the Shrewbury box, but referee Mike Ryan booked him for diving.
Campbell on his return from injury, forced Edwards into a full length save from 25 yards, then at the other end Van der Geest pulled off an equally good save from Jemson from the same distance.
There was a let off for Quakers after 61 minutes when slack play allowed Micky Brown to cross from the right for substitute Luke Rodgers to head just over the bar.
However, Quakers ensured victory after 78 minutes when substitute Garry Williamson played the ball into the Shrewsbury box for Hodgson to pull back into the path of Marsh to stab in.
Former Hartlepool striker Chris Freestone, who came one as a substitute near the end, almost pulled a goal back, but first Van der Geest turned his close range shot away and in the last minute Freestone blazed wide from ten yards.
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