I'm on mobile so I apologize for no sources and the brevity. The short of it is, despite his radically anti-monarchical views, he had friends in Parliament--including Andrew Marvell--that vouched for him and convinced Charles II not to execute him. While Milton's works were burned and suppressed under Charles II, they were not expunged from history of course. After the Restoration, Milton still wrote, but his works were far less radical.

TL;DR He had friends in high places.