Aldershot defender Darren Jones headed his first goal for the club to salvage a point and extend his side's unbeaten run to seven games.
Rory Boulding's composed finish gave the visitors a half-time lead, while Jones' header was one of the few chances created after the interval as both sides defended stoutly in a dour affair.
Accrington, now unbeaten in their last four league games, took the lead in the 17th minute when Boulding ran on to a fine through ball from Sean McConville to slide the ball beyond Shots goalkeeper Jamie Young.
Jimmy Ryan sidestepped two defenders on the edge of the penalty area and fired in a low drive that crashed back off the post in the 30th minute.
The Shots improved as the match wore on and Jones flicked home an Anthony Straker free-kick past Accrington goalkeeper Alex Cisak in the 52nd minute.
Stanley had the better chances to win it late on, Young denying McConville before Boulding tumbled in the area under pressure from Jones but no penalty was given to the frustration of the away bench.
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