Bonanza 35 pilot reported an engine failure during cruise at 6;500 feet resulting in a divert and engine out landing.

Narrative

Flying at 6;500 ft. MSL; level cruise. Smelled a burning odor. Did not see anything unusual on engine/aircraft instruments. As a conservative measure I turned back toward ZZZ; my departure airfield. Shortly after the turn; I checked in with Approach; stated my intentions to return to ZZZ; and took some avoidance vectors from Approach for traffic. After clearing the traffic; I checked my engine instruments again and noticed zero oil pressure. I then pulled the throttle to idle; pulled fuel mixture to cutoff and just before I turned the key to off; the engine shuttered and made an unusual noise. At this point the engine was inoperative. I [requested priority handling] with Approach and asked for nearest airfield. I was about 1 mile from ZZZ1. I began a spiral descent over the airfield and called ZZZ1 UNICOM and stated my condition with intention on landing at their airfield. Spiral descent; flap/gear configuration and landing were all uneventful. I cleared the Runway with sufficient inertia from the landing rollout and came to a stop on the Taxiway.