The Law of Supply (LOS) and the Law of Demand (LOD) are the two most successful economic predictions. I know you asked for one example, but these concepts run hand in hand, and are often thought of as one general concept. One of the earliest mentions of ideas like LOS and LOD was in 1691 by the philosopher John Locke in his publication "Some Considerations on the Consequences of the Lowering of Interest and the Raising of the Value of Money." However it was noticed well before then (it just wasn't in a published work).
The LOD says that if the price of a good decreases, the quantity demanded for that good will increase (as long as consumers are able to purchase more). This prediction has been realized more times than we can count. There is really only one exception to the LOD, and that is giffen goods. However, seeing that there are only a handful of cases where a giffen good has been observed, they make up a minute fraction of the total number of observations.
The LOS says that if the price of a good increases, the quantity supplied for that good will increase (as long as firms are able to produce more). Again, this prediction has been realized more times than we can count. I cannot think of any exceptions to the LOS.
These two laws are the most successful predictions in economics (in my opinion) because they are the basis for all of economics. If these two laws were not true, most of economics wouldn't be as it is today.