The Reds went in two goals down at the break after falling behind when Lionel Ainsworth's cross was headed past Alan Fettis by James Collins at the far post. Coach Fettis, playing as Tomasz Kuszczak and Joe Coll were ruled out, was beaten again when he saved Sean McAllister's initial effort but had no chance with the rebound.
United spurned chances in the opening period with John Cofie blasting over the bar on 24 minutes and Will Keane heading off target from close range following a corner by Danny Drinkwater.
Midfielder Drinkwater, who scored at Curzon Ashton last Monday, reduced the deficit soon after the restart with a fierce drive from outside the box that hit a post and went in off the back of keeper Chris Neal.
Despite first-teamer Darron Gibson playing the full 90 minutes as captain, the visitors were unable to find an equaliser and were indebted to Fettis for keeping hopes of a draw alive with a couple of fine saves towards the end of an entertaining game on a cold afternoon in Shropshire.
United: Fettis; M.Keane, McGinty, Fryers, Thorpe; Drinkwater, Pogba, Gibson, Petrucci (Lingard 55); W.Keane, Cofie (Cole 46). Subs not used: Massacci, Giverin.