A B737-700 Captain shut down the right engine after landing to save fuel. Upon entering the ramp area he shut down the left engine to save even more. Used the APU to restart the last engine and complete the taxi to the gate.

Narrative

While on taxi towards the gate area at our destinationI shut down the #2 engine after a cool down period. While entering the ramp area; I had my hand over the #1 start lever. The #1 engine was at idle. During this time we were looking outside to ensure the ramp safety zone was clear. It was dark out. While entering safety zone; and in anticipation of the Marshaler's hand signals; I accidentally hooked my finger on the remaining engine start lever. This happened while my hand was near the engine start levers. I felt the lever move slightly; I pushed it up to its normal idle position; but the aircraft engine began to roll back and shut down. I stopped the aircraft about 15 feet short of the parking spot. The aircraft was on APU power so while stopped; we restarted the engine. Then we proceeded to parking and de-planed normally. I think it is somewhat common for the Captain to have his or her hand on or near the start lever while on the ramp; but this is a bad procedure; especially if only one engine is running. Perhaps the First Officer should shut down the right engine and hydraulic pressure after shutdown while the Captain stays heads up. In any case; I will be extra cautious in the future.