The second-seeded Pole, looking to win her first grand slam title, next faces 19th-seeded American Sloane Stephens or Bulgarian Tsvetana Pironkova.
Highlights: Radwanska overcomes Strycova in three sets
Following an early trade of breaks, Radwanska pulled away, winning four consecutive games to bag the opening set before opening a 3-0 lead in the second.
But she completely lost her composure and world number 33 Strycova reeled off five straight games on the way to taking the tiebreak.
Order was restored in the decider, however, as Radwanska broke four times to wrap up the win.