The cash-strapped Cherries picked only four subs including schoolboy Jayden Stockley, who came on for a first taste of league football three minutes from time.
But they started strongly and 19-goal Brett Pitman was a whisker wide from 25 yards early on and after heading a good chance onto the top of the net, he also blasted an easier chance over from six yards.
Shwan Jalal twice saved brilliantly from on-loan Norwich striker Jamie Cureton, who also had two shots blocked on the line.
But the Shrews went ahead shortly after the break when Dunfield fired home from 15 yards to celebrate his recall to the side in fine style.
Shrewsbury finished strongly as Jake Robinson hit the post and Lewis Neal had the rebound cleared off the line. Neal then hit the post two minutes from the end.