Dons striker Ryan Lowe scored a brace to cancel out Tom Eaves' early double but Antony Kay needlessly volleyed past his own goalkeeper in the 69th minute to gift the Shrews their first win in four games.
The result moved Shrewsbury seven points clear of the League One relegation zone and further dented the Dons' slim play-off hopes.
Turner said: "It's a fantastic result for us. It was a game where we had to set the team up properly and for 25 minutes I thought we did just that.
"The negatives are that we've conceded from two set-pieces but the positives are that it's a terrific result and there was some good play in it - we played at times with a little bit of confidence.
"Tom (Eaves) can do that, he was terrific. When you look at his record at Bristol Rovers, I think it was seven goals in 14 games, he's capable of scoring.
"It's taken him a little bit of time to settle into it but he's strong, he gets hold of it, he's got a little bit of pace and obviously an eye for a goal.
"We're due a bit of luck and that was probably it (the winning goal).
"With most of the teams around us not playing we've opened the gap a little bit further - we're seven points above Oldham now. The teams behind us have got a lot of catching up to do and we're in a good position now."