Now Temperature Gauge Says Car's Overheating

Replaced One-wire Coolant Temperature Sensor with a Two-wire Sensor -My car had been stalling at stops, randomly changing rpm's while being driven, and hard idling badly. Several people suggested that I replace the engine coolant temperature sensor. I had recently added a new air filter, spark plugs, spark plug wires, PCV valve, fuel filter, and thermostat, and a few years ago the EGR valve had been swapped out for a different one. The original ECT sensor had only one wire coming from it, but I was assured by AutoZone that their two-wire sensor with included pigtail connector would work. Its directions stated I should connect either of its two wires to my car's existing signal wire, then attach the other wire to a ground. Here's where the problem begins. I've swapped its two wires between signal and ground just to be sure they weren't switched. I tried running it with only one of each of its wires. If the signal and ground are both connected, the car runs perfectly without hard idling or triggering the Service Engine Soon light and Low Coolant Light, however, the temperature gauge skyrockets within 5-10 seconds and stays red-lined even though the engine doesn't seem hot. If the ground is disconnected, leaving only the signal wire, both warning lights appear and the car idles violently for a few seconds before stalling out. Did I receive a faulty ECT sensor, am I not hooking it up correctly, or is it not even possible to replace a one-wire with a two-wire sensor? Please offer me any suggestions you may have.