Two goals in the final seven minutes by Shrewsbury substitutes Ryan Lowe and Jody Banim helped Jimmy Quinn's men leapfrog back into the play-off places in the Nationwide Conference.
However plucky ten-man Margate deserved more, as they were a man short for the entire second half after the dismissal of striker Che Stadhart in first-half stoppage time.
A straight red card looked a harsh decision by Surrey referee Paul Melin, as the former Gravesend man seemed to take one touch too many and his momentum carried him into contact with keeper Scott Howie.
The former Bristol Rovers shot-stopper needed treatment but Stadhart seemed unlucky to be sent off.
Shrewsbury should have led as early as the 13th minute when the highly-rated Luke Rodgers squandered a penalty after Billy Edwards had brought down the dangerous Sam Aiston in the box.
Edwards was yellow carded for the challenge, but Rodgers' spot kick was poor as he sent it wide of the upright.
Rodgers and Shrewsbury player-manager Quinn had a quiet afternoon with the former eventually substituted by new boy Banim just past the hour mark.
Margate were well-served by on-loan midfielder Lenny Piper. The Dagenham midfielder ran the show for the home side who suffered an early blow when losing skipper Graham Porter with a badly bruised jaw after a clash with Shrewsbury's Jake Segmore which earned the midfielder the second yellow card of the afternoon.
Defender Darren Moss was the third visiting player to be booked inside the first half-hour in a feisty affair played on a difficult Dover surface being used for the second successive day.
Margate kept battling away in the second half and Piper headed against the woodwork on the hour and defender Greg Oates fired wide after good work by John Keister and Piper.
Banim, signed from UniBond League side Radcliffe Borough, came off the bench again after an impressive debut against Telford United in the midweek Shropshire derby and shot just wide within five minutes of stepping onto the pitch.
Margate deserved something for all their hard work but Shrewsbury went in front with seven minutes left, Lowe giving them the lead with a right-foot shot that went in off keeper Phil Smith.
Then with the keeper up in the Shrewsbury penalty area for a free-kick, the ball broke quickly and Banim scored to complete a more than fortunate victory for the former Nationwide League side.