You are right. Those words are not found commonly in the suttas, at least to my knowledge.
May be the reason is that when one truly understands Dhamma (basically the unfruitful nature of this world) or pariyatti, one will automatically gets into practice (patipatti), and one will inevitably realize the fruits (pativedha).
Most of the time is spent in learning the background material, getting rid of the 10 types of mica ditthi, and then truly understanding Tilakkhana: the unfruitful, suffering-filled, nature that tends to make one become helpless in the rebirth process.
When one gets to that stage, all three are fulfilled to some extent. It is just a matter of time (relatively speaking), when they are fully completed.
However, there is another way of looking at this: In order to understand Tilakkhana (and to get to pariyatti), one must first follow the mundane eightfold path and get rid of the 10 types of mica ditthi. That goes hand-in-hand with living a moral life. So, at that level, pariyatti and patipatti can be said to go together first.
Then when one starts on the Noble Path by almost simultaneously getting to fulfilling all three to some extent.
Just my initial thoughts. I had never thought about it much before you asked the question.