Not really, at least not from an academic point of view. C showed up a few years after languages like LISP and Simula and around the same time as Prolog. Those languages are far more innovative than C. C on the other hand basically took well known concepts from BCPL and PDP Assembly and improved on them and made them portable.

Unix was basically a simpler, easier to use version of MIT Multics, designed for the smaller and cheaper PDP-7. Most of the innovative ideas in Unix had first implemented in Multics.

So while neither C nor Unix where truly innovative, even for their time, they won out because they took well known concepts and actually made them work in a practical sense.