Phylogenetics does not make any sense as evidence for evolution. That's not what it's meant to be. Phylogenetics is what we do once we know evolution has occured. It's all about techniques to figure out how.
Eh, I mean that's kind of a sweeping statement. There are a number of ways phylogenetics makes sense as a confirmation of the broad theory of common descent.
E.g., I conducted molecular phylogenetics research on a set of prokaryotic transporters. The phylogenies weren't congruent with the species phylogeny as established by dozens of well-conserved proteins. This suggested horizontal gene transfer, and when I hunted for signs of HGT (based on GC content analyses), they showed up exactly where one would expect if the species phylogeny was correct (p = .04, based on independent samples t-test).
These results really only make sense under a model of common ancestry -- and it is, in fact, what one would predict under that model.
There's plenty of other examples that could be cited, too. Mol phylogenetics is widely used by evolutionary biologists as a tool within the theory of evolution, but it has also stridently confirmed the theory of common descent.