A B767-300 First Officer shutdown both engines prior to gate arrival. He mistakenly put the left engine fuel switch to OFF; attempted to stop the shutdown but then moved the right engine fuel switch OFF.

Narrative

Our scheduled departure from the South American station was XA:05 local time. We were informed that the aircraft would be late arriving; so we delayed our departure from the layover hotel. The new expected departure time was XE:30 local. However; the plane arrived with a mechanical problem. After an additional delay to repair the plane we departed at XG:48 local time. We were 6:43 later than our scheduled departure. After flying an all night international flight that was delayed over 6 hours; I made an uneventful approach and landing. As we approached the lead in line for the gate; the Captain asked me to shut down the RIGHT engine in keeping with normal standard operation procedures. I first had to set up the Air Conditioning Panel for the engine shutdown. Then I reached down; without looking; and moved the LEFT fuel shutoff switch to cutoff. As the switch approached the stop I glanced down to see that I had grabbed the wrong switch. So I tried to quickly return the switch to run. Then I turned off the RIGHT fuel shutoff switch. However; the left engine had already shut down; and now the right engine was shutdown. BOTH ENGINES WERE OFF AS WE APPROACHED THE GATE. At this point the Captain stopped the aircraft; set the parking brake; and asked to be towed into the gate. Lessons learned: 1. Slow down while activating switches in the aircraft. Don't rush. 2. Always look at the switch I am moving. Never go by feel. 3. Be aware of fatigue issues.