Newton was really no more "secularized" than Kepler, to be honest — he just played his cards closer to his chest, because he was afraid of being persecuted for his (at the time illegal) beliefs. He saw his work in astronomy, alchemy, and theology as tightly interlinked, just different aspects of the same thing and the same motivation.

He and Leibniz had great disagreements about the religious import of their work; Newton actually saw the complexities of multi-body systems as indicating the existence and need of an actively-intervening divine creator (to keep it from descending into chaos), where Leibniz thought that Newton gave God too little credit in creating stability.

The explicit "secularization" of astronomical work took place sometime after Newton and Leibniz, in the 18th century. The French Enlightenment is given a lot of credit for this. The French philosophes, notably Voltaire and Madame du Chatalet, saw in Newton what they wanted to see: a thoroughly secularized genius who discovered the equations that ruled the heavens. This is not what Newton was, at all, but it is how they "translated" Newton (even literally) into French. Much of what the world came to understand about Newton came out of this tradition (it was only in the 20th century that his work on alchemy and religion became well-known and better understood).

This occurred at about the same time as the Chemical Revolution and a general reorganization of scientific practice in the Western world that created the "boundaries" that we think of existing today between, say, chemistry and alchemy, astronomy and astrology, science and religion, etc. This "boundary work" (as historians sometimes refer to this) was ahistorical (in that prior to the 18th century it was entirely possible to be both a chemist and an alchemist, like Boyle, or an astronomer and an astrologer, like Kepler), and not even entirely accurate (the science/religion divide is not quite a real one, either historically or even presently), but served the Enlightenment propagandists' purposes very well, setting them up as the new, liberated minds of the future. This of course lead to its own bloody outcomes by the end of that century, and in the 19th century the promoters of science took up these distinctions even more firmly and used them as a cudgel to promote the interests of an autonomous, separate-from-everything (religion, politics, etc.) "Science" with further propaganda that we still see remnants of to this day (e.g. the whole "Science vs. Religion" debate and the many myths associated with it).

So in a sense this is not quite a real distinction, though it is definitely true that during this period many of the "mystical" aspects of scientific practice got thoroughly jettisoned (like astrology). But I wouldn't see this as a distinct break, and rather a gradual process — as you move through the 17th century, you start to see a heavier reliance on quantitative and "naturalistic" explanations of scientific phenomena, and an increasing skepticism of the more "out there" claims of alchemists, astrologers, etc. It stops being part of the profession, though not entirely; again, the line between a chemist/alchemist is still very fuzzy, and to suggest that astronomers were doing anything towards purely secular ends strongly overstates it. By the 18th century, with new methodologies and expectations and a "revolutionary" redefinition of themselves, you start to see these strands of work being explicitly excommunicated from the definition of science, and this is largely taken up by "men of science" in the 19th century.