Tranmere needed a Chris Shuker goal after 69 minutes to finally break Accrington's resistance and progress to the FA Cup second round with a 1-0 win.
There were early chances for both sides, with Rovers' Ian Moore unlucky to hit the crossbar with an excellent chip over keeper Kenny Arthur in the fourth minute, before at the other end Danny Coyne made a fine diving save from a well struck effort by John Mullin.
Steve Jennings and Moore volleyed wide for the home side before a back-heeled effort by Stanley sub Colin Murdock following a free-kick was only a foot off target.
Tranmere sent on Ed Sonko and adopted a more attacking formation after half-time, but it was the visitors who nearly broke the deadlock after 67 minutes when a James Ryan shot struck a post.
But two minutes later Tranmere were ahead with an excellent angled finish by Shuker when set up by Jennings after a flowing attacking move.
Sub Chris Greenacre went close to a second for Tranmere in the 90th minute but Arthur saved well.
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