Alex had taken the lead in the 19th minute when on-loan QPR striker Tom Hitchcock nodded home from the six-yard line after great work by Mesca Bangna and Chuks Aneke.
But the visitors pushed hard for an equaliser, with Luke Summerfield twice firing wide before Jon Taylor forced a stunning from Crewe keeper Ben Garratt from point-blank range.
After the break Graham Turner's side deservedly levelled as Taylor ran on to a long ball before smashing into the net.
Shrews had the momentum, but it was Crewe who went in search of a winner, although they they failed to test the keeper, with Aneke most guilty as he missed a hat-trick of chances.
Shrewsbury should have won it in time added on, but Tom Eaves could not get enough power on a lazy stab that led to a comfortable save.