Wanderers piled on the pressure in the second and were indebted to midfielder Sheehan’s sweetly struck 63rd-minute effort.
Marko Marosi prevented a wider margin of defeat for Steve Cotterill’s visitors, who have won only once in their past ten matches.
“We said at half-time, if they are going to offer us shots from the edge then we should take them,” revealed Evatt.
“We wanted to be more proactive with that and Josh put it away brilliantly.”
Kyle Dempsey twice went close in an otherwise frustrating opening half for the Trotters. But with the Shrews tiring, the chances became more frequent after half-time.
Marosi’s second-half save denied Dion Charles and the home side’s top scorer also had a goal disallowed for a foul.
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