Wayne Curtis scored twice to earn Morecambe a share of the spoils.
A Curtis penalty pulled Morecambe level at 1-1 after Ryan Lowe's fierce drive had given the Shrews the lead.
Jake Sedgemore's penalty put the visitors back in front, before Nicholas Rogan's superb drive from the right-hand side of the area made it 2-2.
Jimmy Quinn's cool finish - after Craig Mawson saved his initial strike - restored Shrewsbury's lead, but Curtis had the final say with a stunning shot.
Morecambe: Mawson, Walmsley, Murphy, Bentley, McKearney,
Thompson, Drummond, Hunter, Osborne, Curtis, Sugden. Subs: Swan,
Stephen Hill, Rogan, McFlynn, Garnett.
Shrewsbury: Hart, Moss, Ridler, Sedgemore, Lawrence, Street,
Tolley, O'Connor, Aiston, Lowe, Quinn. Subs: Banim, Rodgers,
Challis, Edwards, Howie.
Referee: D Drysdale (Bracebridge Heights).