C172 Pilot reported an inability to control engine throttle during a maintenance check flight. After diverting towards a nearby airport and a landing was assured the pilot used mixture to control engine speed; then shut down the engine; and glided to a safe landing.

Narrative

While performing a maintenance new engine break in with a flight club mechanic and while at cruise 7;500 ft. msl; upon attempting to reduce power in order to descend I realized we were getting no response from our throttle. The RPMs were indicating ~2;300 RPM and as I pulled the throttle back; got no change in power output. I pulled throttle all the way to Idle and still got no change in RPMs. I enriched and leaned the mixture and got power changes to RPMs. Mag check was fine; all engine indications were what would be expected at cruise. I called ZZZ Approach on XXX.XX to tell them of the problem we were having and told them we would be diverting to ZZZ. I descended to ~ 6;400 ft. MSL and over flew the field to check wind direction. Once it was determined the winds were out of the east; we flew west bound to set up for a straight in for Runway X. I decided to fly straight in and as we got closer to the runway began leaning the mixture knob to the point of getting an RPM drop in order to slow down enough to add flaps for landing. Once we were assured of making it to the runway we shut down the engine and glided in for landing. No issues on the landing and had enough momentum to clear the runway. [An airport tenant] came out to the airplane and helped us push it to his hangar. The Mechanic I was with borrowed tools from the Good Samaritan and removed the cowling to check for the problem. While he was doing this I phoned ZZZ Center to tell them we had landed safely with no damage or injuries to us or the airplane. Upon investigation it was determined the problem was with the throttle linkage. He fixed the problem and we flew home uneventfully to ZZZ1.