Williams has not made it as far as the quarter-finals since 2010, but this year has seen the 34-year-old in resurgent form at Melbourne Park.
Williams notched a 6-3, 2-6, 6-1 victory over Radwanska, and hopes her success at the Australian Open is the beginning of a trend that will see her continue to win in 2015.
She said: "I want to be playing deep in all my events. Everybody wants that. Now is my moment and I want to keep this moment going all year and then next year too.
"I think I played well when it mattered. Her style of game was completely different than the first three players I played.
"The first three players I played tried to blast me off the court. This was the first time there was any sort of rhythm at all. The way she hits the ball is so different. A lot of times, especially for a player like me, you feel like, wow, why am I not hitting more winners?
"That's not just always the answer. It's definitely a balance between being aggressive and being patient and being smart because the way she plays is very deceptive. Not everyone plays that way."