I had the same problem a few days ago and it was because my zone valve had not totally sealed after the last watering. Try activating that zone and shutting it off again. You should be able hear if any water is seeping through that valve (kind of a whisping sound). If it still leaks you may need to clean the zone valve for dirt or other crap that can get in there. this is not a leak in the actual zone itself, if it was you would only notice leaking when that zone is activated cause that is the only time it is charged with water.

In regards to your other question you should not have to turn the house water off as the sprinkler system should have its own main shutoff valve seperate from the house shutoff.

The automatic valve(s) are either on a manifold (in one location) or located separately inground in the general area of the individual zones. If the wet spot is located near the farthest head on that zone, then I would guess that the particular valve for that zone is not shutting down completely. Locate the valve, wherever it may be, and listen carefully for a low hissing sound. Back off the bleed screw located on the discharge end of the valve and the whole zone should come on. If you did hear that hiss, then locate the shutoff valve for the whole system (usual) or the zone (less common). When the water is shut off, you can check that the solenoid is operating properly (look out for an 'O' ring in the recess of the solenoid port) and that the orifice is clear. You can flush it by turning on the water and look for a jet of water. If that does not resolve the problem then you will have to go into the valve; which is not difficult but I would recommend that you practice on an old valve. Regardless of the make, the general construction is similar. You can obtain a "guide to sprikler installation" from any hardware store. It helped me to understand the name and function of the many components.