If your best friend pulls up beside you in her convertible just as your bike gets a flat tire, you could call it providential, or magically lucky.
The Latin root of providential is providentia, "foresight or precaution." Providence changed over the years; it usually referred specifically to the care of God, and it was spelled with a capital P. Providential, likewise, has another meaning that's purely religious, "resulting from God's intervention." Whether you're talking about God or not, if something is providential, it feels a little miraculous.