Two goals in 11 first-half minutes did the job for Stephen Robinson’s players as they continue to adapt to life in the third tier.
Adam Phillips netted the opener from the penalty spot on 34 minutes before Cole Stockton made it four goals in a week with half-time moments away.
Robinson made four changes from the side which defeated Blackburn Rovers in the midweek Carabao Cup meeting.
Back came Ryan Cooney, Toumani Diagouraga and Arthur Gnahoua, while Rangers loanee Josh McPake made his debut for the Shrimps.
A boisterous crowd, the majority of whom were at the Mazuma Stadium for the first time since February 2020, welcomed Robinson’s players, who were looking to build on their opening-day point at Ipswich Town.
It took them only 71 seconds to have the first effort at goal, Cooney placing his shot wide from the edge of the area.
Robinson had warned in advance about the danger Shrewsbury would pose, especially from set-pieces, and they twice came close to proving him correct in the opening quarter-hour.
A free-kick was only half-cleared and Josh Vela lobbed over from 20 yards before Aaron Pierre headed a corner wide from six yards.
After that start, the game developed into something of a slow burner for a while with both sides cancelling each other out.
It was the Shrimps who were playing the better football, however, and that led to them opening the scoring.
Diagouraga’s delightful pass released Phillips, who was hauled down inside the area by Nathaniel Ogbeta.
Referee Declan Bourne eventually pointed to the spot and Phillips sent Marko Marosi the wrong way from 12 yards.
Gnahoua curled another effort straight at Marosi before Morecambe doubled their lead on 44 minutes.
Another fine move ended with Gnahoua’s cross being blocked for a corner, which Shrewsbury didn’t deal with and the ball dropped invitingly for Stockton to score.
The visitors’ response at half-time was to introduce striker Sam Cosgrove and they started the second period on the front foot.
Rekeil Pyke saw a shot blocked and a lovely team move caught out the Morecambe midfield, only for Luke Leahy to overhit the final cross.
Pierre headed another corner off target but, with the game entering an increasingly open phase, the Shrimps could have put the game out of sight in a five-minute spell.
McPake had an effort held by Marosi, Stockton missed his kick from Gnahoua’s cross and a penalty appeal was waved away when Phillips went down under pressure from Pierre.
Stockton also attempted a carbon copy of his first goal at Ipswich but, on this occasion, his effort was beaten away by Marosi.
Wes McDonald replaced the impressive McPake and attempted to catch out Marosi late on, only for the keeper to save his effort at the near post.
There was still time for the Shrews to see Matthew Pennington’s shot deflected behind and Cosgrove to fire over.
That was as close as they came as, despite four added minutes, the Shrimps held them at bay to claim three points.
Morecambe: Andresson, Cooney, O’Connor, Lavelle, Leigh, McLoughlin (Wootton 90), Diagouraga, Phillips (McCalmont 63), Gnahoua, Stockton, McPake (McDonald 77). Subs not used: Letheren, Mellor, Jones, Harrison.
Shrewsbury Town: Marosi, Pennington, Pierre, Nurse, Bennett (Bloxham 82), Davis, Vela, Ogbeta (Cosgrove 46), Leahy, Udoh, Pyke (Daniels 60). Subs not used: Gregory, Burgoyne, Caton.
Referee: Declan Bourne.
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