Both goals came in the second half when Accrington stepped up a gear and Paul Mullin and Jimmy Ryan netted.
The first half was a terminally dull affair. Neither team seemed to possess the craft or flair to unlock the other defence and goalmouth action was very limited.
But it all could have been so different had Mullin put away a decent early chance.
The Accrington midfielder got clear of the defence but could only manage to pull his shot tamely across goal.
A superb block from Paul Morgan denied Jamie Clarke with Macc keeper Jon Brian stranded, while at the other end Martin Gritton had the ball in the net only for it to be ruled out for offside.
Ten minutes before the break, Accrington seemed to have carved the visitors' defence open when John Miles got clear down the left.
But from his cutback, Andrew Procter's 20-yard effort was deflected well over the bar.
Accrington were a different side in the second half. They began with real purpose and were ahead within five minutes when Mullin volleyed home Miles' corner at the far post.
Stanley proceeded to pile the pressure on the defence and it only took them 10 minutes to crack.
From another Miles corner, Ryan fired in a decent 25-yard effort and Brian made a complete hash of his attempted save before fumbling the ball into the net.
The rest of the game was a stroll for Accrington, although Kenny Arthur pulled off a good save at his near post to deny Gareth Evans five minutes from time.