Derek Adams’ side looked more than a match for the hosts until they shipped their first goal on 43 minutes.
The game went downhill quickly from there with two goals each from Luke Leahy and Daniel Udoh and Ryan Bowman’s header giving the final scoreline a one-sided look.
The home side worked the ball down the left and George Nurse got in behind Shane McLoughlin to drill a low cross into the area for Udoh to score from close range.
Tom Flanagan’s long-range shot was adjudged to have hit the hand of Jacob Bedeau and Leahy sent Trevor Carson the wrong way from the spot.
Things then became worse for Morecambe when they shipped a third on 51 minutes with Leahy scoring his second of the game.
The Shrimps failed to clear their lines once again and Leahy curled a superb effort into the top right-hand corner of Carson’s goal from the edge of the area.
To make matters worse, Shrewsbury made it 4-0 in the 65th minute.
Udoh scored his second of the night with a superb turn in the box before drilling a fierce shot into the roof of the Morecambe goal.
Ryan Bowman then made it 5-0 20 minutes from time when Leahy delivered a far post cross and the striker beat Bedeau in the air to head past Carson.
The Shrimps failed to produce a single effort on goal as Steve Cotterill’s side picked up their biggest league win of the season and Morecambe remained deep in the relegation mix.
Shrewsbury Town: Marosi, Pennington, Ebanks-Landell, Flanagan, Bennett (Daniels 74), Vela (Whalley 66), Fornah, Leahy, Nurse, Udoh (Bloxham 66), Bowman. Subs not used: Burgoyne, Pierre, Bondswell, Janneh.
Morecambe: Carson, Bedeau, O’Connor, Gibson (Mensah 83), McLoughlin, McCalmont (Cooney 66), Diagouraga, Leigh, Wildig, Connolly (Ayunga 74), Stockton. Subs not used: Smith, Obika, Gnahoua, Fane.
Referee: Darren Drysdale.