B737-700
Flight Crew Instrument; Flight Crew Air Transport Pilot (ATP); Flight Crew Multiengine
Flight Crew Last 90 Days 437
Workload
Aircraft Equipment Problem Critical
Air Traffic Control Provided Assistance; Flight Crew Diverted; Flight Crew Requested ATC Assistance / Clarification; Flight Crew Overcame Equipment Problem; Flight Crew Landed in Emergency Condition
Aircraft
Approximately 60 miles northeast of ZZZ at FL 380; the #1 engine rolled back to 68% N1. The engine would not respond to forward thrust lever movement; only to a lower thrust lever setting. Since this partial engine power was not addressed specifically in the QRH I thought that turning off the associated EEC (Electronic Engine Control) might allow us to regain control. The EEC was turned off; without effect and was turned back on. The decision to divert to ZZZ was an easy one. The Flight Attendants and Dispatch were notified. ATC was advised; vectors were provided to a Runway XX arrival.  The engine failed completely on downwind.The Engine Failure and One Engine Inop Landing QRH checklists were accomplished. The First Officer was the Flying Pilot; he continued to fly and did most of the communicating with ATC. Performance calculation flaps 15 engine out data was used and briefings completed. Aircraft control was transferred and I became the Pilot Flying.  A normal engine out flaps 15 landing was made. After clearing the runway; ZZZ Fire Rescue looked over the engine and detecting no threats; we taxied to our assigned gate.Two passenger PA's were made while airborne and one after landing. There were no Passenger issues that I was made aware of; our Flight Attendants must have done a wonderful job. My First Officer did a perfectly professional job of flying and communicating with ATC. KUDOS to all the SIM Instructors I have had over the years.
B737-700 Captain reported loss of power in the #1 engine while at cruise altitude which caused a diversion.