What would be the process of getting OUT of an accepted job offer?

Quick summary, I was offered a job last night and received the written offer this morning. I plan on accepting the offer as it’s a really good pay raise, a new shift (3rd) which I could use the change, and it has much more opportunity for advancement than my current position. The only possible hang up is if my current employer counter-offers and matches or even exceeds the new employment offer (which while I think is unlikely, I doubt it’s impossible).

The hang up now though, is that my boss is out of work for the day. I don’t want to leave the new employer hanging at all, I want to sign the offer acceptance and get it back to them ASAP so they don’t wonder whats going on. But if I do that and then tomorrow I tell my boss and he counter offers something I would accept to stay…

What would be the process of getting out of an acceptance of the employment offer, IF it would all come to that? Has anyone got any experience in this matter?