Goals early in each half from Stuart Nicholson and Dave Hibbert from the penalty spot enabled Shrewsbury to secure the points and maintain their place among the League Two pacesetters.
But for struggling Accrington it was an afternoon to quickly forget, as they had five players booked and midfielder Jay Harris ordered off three minutes into the second half.
Shrewsbury made a dream start, assisted by some woeful Stanley defending. After just three minutes the visitors failed to clear their lines and the hesitancy was to cost them dearly as Marc Pugh crossed into the goalmouth where Nicholson was on hand to nudge the ball home from close range.
Accrington made a spirited attempt to play their way back into the match after the early setback, and impressive centre-back Mark Roberts headed just over, and striker Roscoe D'Sane denied by a last-ditch tackle as he closed in on goal.
But their defensive frailties remained and Hibbert should have increased the home side's advantage when he pounced on a poor back pass from Stanley skipper Peter Cavanagh, only to see his drive from 10 yards strike a post.
Accrington's task became even harder when they were reduced to 10 men on 48 minutes, referee Hall showing Harris a straight red card for his foul on Marc Tierney.
Any hopes of salvaging at least a point evaporated further four minutes later, when Cavanagh sent Pugh crashing in the box, with Hibbert safely netting the resulting penalty.
The last 20 minutes was mainly one way traffic toward the Accrington goal, but Shrewsbury were denied any further reward as Stanley keeper Kenny Arthur proved himself equal to efforts from David Hunt and substitute Michael Symes.