Similarly to

• The first transistors in space: Germanium or Silicon? What about in orbit?
• First LED left on another planet⁺ by humans? w/list of space electronic "firsts" questions
• First TTL chip in space and in orbit? Was it a 7400 series or something that predates?

which mission used the first multiprocessor in space?

The Saturn control computer used three processors executing the same program to increase reliability by redundancy.

This question is about the first distributed computing in space, several processors executing different programs.