Josh Low's early effort proved to be the Robins' only goal, although they could have wrapped up a convincing victory had they taken a string of chances in the League Two clash at Whaddon Road.
Low struck after just nine minutes when he collected a pass from Justin Richards before firing into the net from 12 yards.
But the visitors drew level midway through the half when Turner powered home a shot from just inside the area.
The home side had a glorious chance to regain the lead just before the break but Julian Alsop saw his header brilliantly saved by Ian Dunbavin in the Stanley goal.
Michael Townsend then went close early in the second period but he failed to find the target with a header from six yards.