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Paul Sturrock's men, aiming to bounce back from a 2-0 defeat to Bradford on Good Friday, left it late but scored twice in the last quarter of the game to seal an important victory.
With 70 minutes gone Luke Prosser nodded Ryan Hall's short corner back across goal and Eastwood was on hand to nod home his second goal since returning on loan from Coventry.
Eastwood then turned provider in the final minute with a pinpoint cross from the left which Grant met with a stunning long-range volley which flew past Seb Brown and into the back of the net.
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