M20 pilot reports throttle linkage failure with throttle fixed at high power setting. When landing is assured engine is shut down with mixture control. Safe landing ensues.

Narrative

Upon takeoff everything was normal; however I felt that the throttle lever was pushing back out. I tightened the throttle friction lock. The plane performed well as expected. When I reached my cruise altitude I noticed that when removing power to cruise power setting that a great amount of throttle removed on the lever was only amounting to a very small change in manifold pressure (1/3 of the travel only produced 3-4 MP decrease). At this point I was thinking that we were having some trouble so we decided to continue on to ZZZ; a few miles away. We positioned over the airport and started to remove power and there was no response other than a slight decrease in MP. After slipping in a descent I put the landing gear down and pulled the power on final approach and glided into the airport. Everything was fine; we restarted the engine to taxi and immediately it went to full power. So we taxied it in and parked the plane. I believe there was a problem with the throttle cable which may have caused the carburetor butterfly to engage full throttle as a protective measure. Our Mechanic will be looking at it shortly to determine the cause. The only way I could have been more proactive would have been to take off the cowl during my preflight; perhaps the problem could have been visually seen. The cowl which has many many screws is not easy to take off and I did look in the engine compartment and checked oil before flight; however you can't really see the carburetor.