Dagenham ended a two-match losing run in style with a devastating display.
Chris Moore opened the scoring just before the half-hour mark, drilling the ball into the bottom corner.
Chris Piper doubled the lead from the penalty spot after Shrewsbury's Darren Moss had fouled Paul Bruce.
Pacquette opened his account with a right-foot shot, Moore added a second and Lee Goodwin completed the rout by volleying home Jimmy Jackson's corner.
Dag & Red: Naisbitt, Cole, Vickers, Goodwin, Piper, Pacquette,
Bruce, Hill, Jackson, Mustafa, Moore.
Subs: Baruwa, Perfect,
Bentley, Watts, McGowen.
Shrewsbury: Howie, Moss, Rioch, Tinson, Ridler, Banim,
Sedgemore, Cramb, Aiston, O'Connor, Lowe. Subs: Dunbavin, Darby,
Edwards, Quinn, Street.
Referee: M Russell (St Albans).