What's a non-religious word for miracle ?

I really hate throwing around a word like "miracle" to refer to things that are no where close to miraculous. 

For example, my gray/white roots are approaching 1 inch in length.  My locally based "not great but does a fine job and is cheap" hairdresser is out of town for a month.

I called my swanky Capitol Hill "used to be my go to hairdresser" but is now "only for special occasions, emergencies, or if I find $200 laying in the street" hairdresser and somehow got an appointment for tomorrow, even though they are still closed today.  The owner was in taking care of some paperwork and just happened to pick up.

But that still leaves my children unattended tomorrow afternoon, so then I was also able to find a babysitter in short order.  Mr. Q is also able to come home from work a little early.

I was trying and trying to think of another word for miracle, because this is not really a miracle, but I just can't get it.

Oh wait !

Lucky !