Stanley went ahead through Terry Gornell early in the second half, but after Collins had equalised the Shrews took over, with Collins adding his second and Mark Wright sealing the win with a third.
Turner said: "We were desperate for that win. We knew when we came here we had to match their endeavour, heart and spirit and we did.
"They caught us cold with their goal but our response was immediate and then we were terrific and looked dangerous on the break and we`ve got to be pleased with the win.
"We drew on Saturday and I felt we had thrown two points away but now four points out of two away games doesn't look too bad.
"James took both his goals well and the front two of Collins and Tom Bradshaw grind defences down and that's what they did in this game. Ben Smith made some superb saves too."