Joe Jacobson headed in a corner to edge Shrewsbury in front before young debutant Liam McAlinden, on loan from Wolves, made sure of maximum points with a cool finish nine minutes from time.
Turner was delighted as his team had thrown points away by conceding costly late goals in all four of their previous matches.
He said: "When the board came up at the end for six minutes of stoppage time and our record of conceding late goals, it was a massive relief when the final whistle went.
"I thought we played well. We were very lively with the ball and we might have had one or two more goals.
"We had to defend solidly as they're a difficult side to play against with their power and the way they play."
Turner saluted the instant impact of McAlinden who quickly delivered after being introduced in place of another Shrewsbury debutant, Spaniard Christian Lopez.
"It's a shame we didn't have Liam several weeks ago because he's a player I've watched for the last 18 months," he added.
"Wolves originally wouldn't let him come out but just recently they could see the way forward for him to come out and get some game time.
"Liam had not had much chance to get to know the players after just one training session but I'm sure both he and Cristian can settle in and make a big contribution."