Billy Kee’s penalty and further goals from Sean McConville and Kayden Jackson gave John Coleman’s side the victory at Blundell Park.
McConville went close just before half-time as he curled a free-kick round the hosts’ wall, but Ben Killip managed to get across quickly to palm the ball away for a corner.
The visitors eventually took the lead just after the break when McConville was tripped inside the penalty area, giving Billy Kee the chance from the spot, and he made no mistake as he sent the goalkeeper the wrong way.
And McConville was again involved as Accrington doubled their lead, with the midfielder latching on to a cross from the right to head the ball into the roof of the net.
Jackson then made sure of the points when he drove into the penalty area from the left and fired high into the net to give Accrington a long-awaited win.
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