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Can I get into a top school C.S. Ph.D. program with a Master's from a lower ranking university?

Is it possible, and what are the chances of doing so, to get into a Computer Science Ph.D. program at a top school like e.g. the U of Toronto with a Master's degree (say, with excellent academic record) from a lower-tier school?

My situation is as follows:

  • I am about to complete my Master's degree in math (GPA will be between 3.7 and 4.0) in a program with a high reputation (acceptance rate 40 out of 170). I have done mainly (functional) analysis and mathematical physics, and some differential geometry and probability theory. No computer science-related stuff. Also, no statistics (so far at least).

  • However, I am increasingly unhappy with my field, and I would like to go into machine learning. I know how to program and I have won some competitions as a high school student at federal state level (Germany), but I haven't taken any university courses in computer science so far.

  • This term I'm taking courses in databases, operating systems and machine learning. That will be enough to get admitted into the Applied Computer Science Master's degree at the University of Heidelberg (note that Master programs in Germany are two-years programs). Certainly not itself a bad university, but the computer science program doesn't really have a very high reputation (after all, there's a reason the admission requirements are so low). With virtually no formal education in computer science, I just don't have a lot of options at the moment.

  • Assuming that I will complete that Master's program with a very good GPA (and also additionally take the one and the other undergrad course like e.g. algorithm design to catch up), what would be my chances to be admitted e.g. into the Computer Science Ph.D. program at the University of Toronto or a similarly good school? At the moment, I would certainly have no chances to be admitted into their Master's program.

I have also considered doing a one-year computer science conversion Master at a better school, but I found the curricula of those programs rather basic and concluded that doing a 'real' Master's at a not-so-good school would be the better option. But maybe that's just my German way of thinking... Here in Germany the name of your schools means relatively little, but my impression is that things are somewhat different in the anglophone world (in particular the U.S. and the UK).

  • Would it increase my chances if I combine this degree with edX MOOCs from top-tier schools like MIT?