Paul Mullin gave Stanley a tenth minute lead only for Shrewsbury to level in bizarre circumstances just after the half-hour mark when Neil Ashton netted directly from a corner. The home side held sway for the remainder of this sometimes entertaining, but more often that not nervy encounter, with a second half Ben Davies goal ultimately clinching three more precious points as Shrewsbury's grip on a play-off place begins to tighten.
Shrewsbury made a bright start and from successive Ashton corners almost took the lead - the first drifting right across the six-yard box, while the second was headed inches wide by Wales Under-21 midfielder Dave Edwards.
So it was against the run of play that Stanley took the lead. Jay Harris saw his close range volley well saved by Shrews' keeper Scott Shearer - but Mullin, who set a club record for appearances last Saturday, was on hand to follow up and score from six yards.
Just as they had done in their previous home match against Milton Keynes Dons, Shrewsbury found themselves trailing to an early goal, but once more they found the resilience to find their way back into the game and following close calls on the visitors goal by headers from Stewart Drummond and Andy Cooke, the home side managed to draw level in the 33rd minute.
Ashton curled in a low corner from the right, which somehow eluded everyone in a crowded six-yard box and found its way into the back of the net.
On the stroke of half-time lively striker Derek Asamoah had a stinging shot well saved by Stanley 'keeper David Martin. But 60 seconds after the break, Martin was beaten by an Asamoah drive that struck the foot of the post and rebounded to safety.
Asamoah, however, turned provider when Shrewsbury went ahead on 62 minutes. When the Accrington defence failed to clear a corner he nudged the ball into the path of Davies - who advanced to score his 11th goal of the season with a fierce low shot.
Shrewsbury had to survive one late scare when Stanley substitute David Brown fired against the woodwork, but otherwise Town safely protected their lead to climb into sixth place - their highest league position since August.