The visitors had an early opportunity to take the lead when Aaron Wildig lifted a cross into the penalty area, but Tom Bradshaw's effort was saved by Stuart Nelson.
Gillingham responded with an effort of their own as a long ball was pumped into the box form Adebayo Akinfenwa, but his header went just wide of the target.
The home side pressed late on in the half and were inches from taking the lead as Cody McDonald found space for a shot, but his effort clattered off the post.
After half time, Gillingham came close to taking the lead when McDonald tried an overhead kick inside the box, but his effort was well saved by Joe Anyon.
The home side pressed again and Bradley Dack came within inches of taking the lead, but Anyon came to his side's rescue again as he made an excellent save to deny the midfielder.
Gillingham did take the lead in the 72nd minute when Adam Barrett headed home from Dack's cross giving Anyon no chance.
However, just four minutes from time Shrewsbury got an equaliser as substitute Miller headed past Nelson to earn his side a point.