General aviation pilot reported a malfunctioning engine while starting a descent. The pilot diverted and landed safely without injury or damage.

Narrative

I was bringing my neighbors plane home he had just purchased from ZZZ1 outside ZZZ2. I was descending into our home airport ZZZ3 after 2.5 hours of flying this leg when at 3000 feet on the south end of a lake and over airport ZZZ4 my engine began to run very rough and vibrate aggressively. Changing fuel tanks and turning on the boost pump had no improvement as well as carb heat and choke. The engine was making about 50% power. I immediately turned for nearby ZZZ airport and switched to the tower. I [requested priority handling] and received priority handling straight to the numbers for XXL. Engine was continuing to miss and vibrate aggressively. One of my two EGTS had gone cold from 1300 degrees to 400 degrees while all other engine instruments remained in their normal operating ranges. I notified the tower of my indications; fuel and souls on board and plan. I remained high at altitude while the engine continued to produce sufficient power to do so. Once above the glide for runway XXL; I began my descent once the runway was assured of if I had lost the engine. The engine continued to run rough until the flare when I pulled it to idle and it actually seemed to run slightly better. Landing was made with no issues; or damage and I was able to taxi clear and to the FBO under my own power. I filed a report. No people or aircraft were injured or damaged.