Cardiff had fallen behind to a Jean-Louis Akpa Akpro penalty, before Joe Mason levelled from close range.
Anthony Pilkington curled a low free-kick home to put City ahead, before Collins' late equaliser.
Cardiff City starting XI (v Shrewsbury): Ben Wilson, Lee Peltier, Sean Morrison, Bruno Ecuele Manga, Scott Malone, Anthony Pilkington, Peter Whittingham, Kagisho Dikcagoi, Sammy Ameobi, Joe Mason, Federico Macheda.
Subs: Simon Moore, Fabio Da Silva, Joe Ralls, Craig Noone, Declan John, Matt Connolly, Aron Gunnarsson, Eoin Doyle, Matthew Kennedy, Deji Oshilaja, Rhys Healey, Robbie Patten, Semi Ajaya.