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The Iron looked out of sorts and were unable to string a series of passes together and rarely looked threatening until the final quarter.
The Shrews opened the scoring after 18 minutes, when Ryan Lowe lobbed the ball over home keeper Sam Russell.
Scunthorpe's best effort of the first half came from Terry Barwick, who turned brilliantly to fire in a shot that thundered off the woodwork.
The visitors looked sharper and Russell did well to tip over a header from Darren Tinson before a fierce shot from Greg Rioch skidded past the keeper's left hand post.
Scunthorpe's equaliser came in the 75th minute when club skipper Mark Jackson, who replaced Cliff Byrne at half time, fired home a low shot at the far post.
And then came the late strike from Kell that sent the Iron through to the next round.