Two direct free kick's inflicted defeat on Town in their first visit to The Wham Stadium in over 20 years, despite a late Warren Burrell equaliser looking enough to have secured a point
Simon Weaver named the same starting XI that took on Tranmere on Tuesday night, with Kayne Ramsay replacing the unwell Lewis Thomas on the bench.
The hosts looked dangerous in the early exchanges with some deliveries into the box causing problems for Town, but the hosts couldn't convert their chances.
One piece of real quality would prove the difference at the interval as Shaun Whalley curled an inch perfect free-kick into the top right corner 28 minutes in.
Most of Harrogate's encouraging play came through Sam Folarin, whose pace once again was troubling the opposition, though Stanley stopper Toby Savin was able to tip the winger's drove round the post in the visitors' brightest moment.
Weaver made three changes at half time as Josh Falkingham, Levi Sutton and Burrell were introduced, with the early stages of the second half showing signs of improvement.
Town had Mark Oxley to thank for keeping the deficit at one after 66 minutes though, the stopper making three saves in a matter of seconds to deny Stanley after only partially clearing an awkward backpass.
With eight minutes of normal time to play Accrington were reduced to ten men when Seb Quirk was shown a second yellow card for a foul on Abraham Odoh, having been booked for taking a throw-in from the wrong place earlier in the half.
From the resulting free-kick Town drew level, Luke Armstrong flicking Falkingham's delivery into a great area that allowed Burrell to get to the ball before Toby Savin and level the scores.
Stanley almost regained the lead just minutes later, but Shaun Whalley's audacious overhead kick hit the inside of the post and bounced clear.
A winning goal did arrive for the hosts though, who struck gold from a set piece again, this time Jack Nolan finding the bottom corner and securing all three points for the ten-men of Stanley.