Date: 201808
Local time of day: 0001-0600
Location: ZZZ.ARTCC, US
Light: Daylight
Aircraft: B737-700
Operator: Air Carrier
Operating under: Part 121
Flight plan: IFR
Mission: Passenger
Flight phase: Cruise
ATC / advisory: Center ZZZ
Aircraft component: Engine
Component problem: Malfunctioning
Reporter organization: Air Carrier
Reporter function: Captain; Pilot Not Flying
Reporter qualification: Flight Crew Multiengine; Flight Crew Instrument; Flight Crew Air Transport Pilot (ATP)
Human factors: Troubleshooting
Second reporter function: Pilot Flying; First Officer
Anomaly: Aircraft Equipment Problem Less Severe
Detector: Person Flight Crew
When detected: In-flight
Result: Flight Crew Diverted; Flight Crew Landed As Precaution
Contributing factors: Aircraft
Primary problem: Aircraft

Narrative: We were enroute to ZZZ and at FL390. We felt and heard a brief thud; then noticed the #2 engine N1 had decreased approximately 8%. We suspected a possible compressor stall. This lasted maybe a few seconds and engine operation returned to normal. We also noticed that the #2 engine EGT had increased slightly. We decided to start a descent just in case we eventually might need to be at a single engine altitude. ATC initially cleared us to FL370 and then to FL310. The First Officer was the Pilot Flying. As power was reduced further; we felt an increase in vibration with a corresponding increase on the VIB reading.We increased power to a mid-position and vibration readings returned to normal. During this time; we also evaluated possible diversion airports; and ZZZ1 was closest with excellent weather conditions as well. We continued descent to FL250 and ran the Engine Limit/Surge Stall Checklist. We followed all pertinent procedures but since engine parameters were normal except for the slightly higher EGT; we stopped at 'Engine Runs Normally.' Just an FYI; The flight attendants and passengers were kept fully informed that we were evaluating what had occurred; and at present; we're continuing to ZZZ.At that point I wanted to send an ACARS message to Dispatch to advise what was going on; and to voice contact us on the ZZZ1 Ops frequency. I get ready to type...'ACARS NO COMM' illuminated. I typed it in anyhow and as I got ready to call ZZZ1 Ops; Dispatch came on line. They were apprised of our situation; would they 'please advise Maintenance Control; and at present we're continuing to ZZZ.' Shortly after finishing with Dispatch it became apparent that a ZZZ1 diversion would be a more prudent plan. While the VIB indicator was still around .6 for the #2 engine; the EGT was creeping up slowly and now about 80 degrees greater than engine #1.ATC was informed of our request to proceed to ZZZ1 and we were cleared direct. While we did not declare an emergency; we did ask to have the emergency equipment standing by. We opted to operate #2 at idle power for the duration of the flight. All appropriate checklists and procedures were accomplished; flight attendants were informed of our divert; that we weren't planning on anything further out of the ordinary and asked if they would please plan as they normally would for an arrival. Passengers were advised we would be diverting to ZZZ1 as a precaution. The single approach was uneventful followed by a normal landing. No brake cooling issues. After landing on Runway XXR and turning from [the first] taxiway onto [the second] taxiway; we were advised by the fire trucks that they saw a flame in the 'tailpipe' of engine #2. We shut the engine down with the start lever; pulled the appropriate fire handle but did not discharge the bottle; and accomplished the proper checklist. The trucks advised the fire was out and we taxied to the terminal. Passengers were eventually deplaned and were to be accommodated on a flight later in the evening.


Second narrative: [Report narrative contained no additional information.]


Synopsis: B737 flight crew reported irregular engine indications led to a diversion.