Prepare yourself in advance of class.
Read the relevant material - the next section not yet covered (in anticipation of new information), and review your notes from the previous lecture, and do this ahead of class. This will give you a chance to read and take notes on definitions, theorems, and working through proofs. Write the proofs out in order to make them explicit enough to understand "down the road", later in the semester (and connect those proofs to the newly covered definitions and theorems). Personally, I had always rewritten my class notes. I find that concepts and information get "etched" in my "brain" through the act of writing: taking notes as I'm listening, rewriting them, taking notes AS I'm reading...moreso than when I do not much else than read and listen.
That way, you will be "primed" for the material covered in the lecture, not necessarily having mastered it, but you will have developed enough familiarity with the material covered in lecture to be able to really listen, having developed a keen sense of what you grasp and don't grasp. You will be prepared to answer questions left over from you pre-class preparation, and for anything you don't understand in lecture, you'll be in a position to ask intelligent, informed questions. So ask away. My general impression has been that professors relish good questions, and graduate level classes are often "seminar format" anyway, where you are expected to interact intelligently (and if not yet, they soon will be!)
So don't think of "homework" as something to do after class, but before class, as well. Between your self-study and your attendance at lectures, you'll be well prepared to complete problem sets, to start working them as soon as they are assigned.
You'll be a "step ahead" of the game with such a strategy!