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Gillingham are stuttering towards safety and suffered another home blow on Saturday.
James Bolton put Shrewsbury ahead early in the second half and Tyrese Campbell got their second.
It was Gillingham’s 11th home defeat of the season, leaving from four points clear of the relegation zone with four to play.
There was one enforced change for the Gills as Billy Bingham replaced Leo Da Silva Lopes, who was ill.
Both teams were on the verge of safety in League 1 pre-match and it was the visitors who had most of the play first half.
Gillingham could have gone ahead early on, however, when Bingham hit a 20-yard shot against the post.
But the Gills would finish the half without an effort on target, with Brandon Hanlan and Dean Parrett both directing Luke O’Neill crosses wide of the mark.
Shrewsbury striker Tyrese Campbell fired a shot into the arms of Tomas Holy and stabbed another effort wide as the Gills defence was stretched.
The visitors were finding space infront of Gills’ back four but Holy wasn’t overly troubled either in the opening half. Luke Waterfall got on the end of a couple of corner kicks but found the roof of the net with one header and went wide with another.
Gills made a change at the break with Elliott List introduced for Bingham. It meant matching Shrewsbury’s wing-back formation.
Holy made a good early save to deny Omar Beckles after Whalley’s free-kick dropped for him in the box.
And it wasn’t long before Shrewsbury were ahead. Whalley played the ball to James Bolton and he guided a low shot past Holy from 12 yards.
O’Neill came close to replying with a free-kick that he curled just wide.
Shrewsbury’s second goal was similar to their first, but it came from the opposite flank, Scott Golbourne finding Campbell and he struck past Holy.
Gillingham’s first effort on target came in the 68th minute, with Eaves guiding Barry Fuller’s cross goalwards but keeper Jonathan Mitchell was well placed.
The Gills struggled to get back into the game but came close to a goal when substitute Josh Rees had one effort stopped on the line and his follow-up blocked.
Gillingham: Holy, O’Neill, Fuller, Ogilvie, Ehmer, Parrett (Campbell 73mins), Bingham (List 46mins), Byrne, Burke (Rees 66mins), Hanlan, Eaves. Subs not used: Hadler, Lacey, Oldaker, King.
Shrewsbury: Mitchell, Williams, Bolton (Sears 80mins), Waterfall, Beckles, Golbourne, Whalley (Laurent 71mins), Norburn, Grant, Docherty, Campbell (Okenabirhie 83mins). Subs not used: Charles-Cook, Sadler, Gilliead, Payne.
Attendance: 4,109 (246 away)