The feeling of avoiding something other than “dodged a bullet”

Let’s say you hand in a business project for your boss before the deadline. You hand it in on a Monday when the boss does not need it until Wednesday. You go home and check your email, only to find you have an unread email from your boss stating he absolutely needs it today. You have just accidentally saved your job. If you had not handed it in today you would have been fired. The thought that you barely avoided being fired on an “early-bird whim” fills you with a type of panic, followed by immense relief.

Is there another term or synonym for this kind of feeling besides the expression “to dodge a bullet”?

Solution 1:

The idioms "a close call", "a close shave" and "a narrow escape" come to mind.

close call - noun [ C ]
​
A situation in which something bad, unpleasant, or dangerous almost happens, but you manage to avoid it:

• It was a close call for residents when a tornado swept through just west of the town.
• Getting to the airport on time was a close call.

close shave - noun [ C ]
​
A situation in which you come very close to a dangerous situation:

• I had a close shave this morning - some idiot almost knocked me off my bike.

a narrow escape
​
A situation in which you avoid danger although you very nearly do not:

• We got out in time but it was a narrow escape.

Cambridge Dictionary

Solution 2:

In the US ( but apparently not in Britain) to luck out means

(colloquial, idiomatic, US, Canada, Australia) To experience great luck; to be extremely fortunate or lucky. I lucked out and got the last two tickets to the big show. - Wiktionary

So when you are telling your friend about it you can say, “Man, I really lucked out today. I decided to turn my project in today instead of Wednesday when it was supposed to be due, and then found out that my boss had actually asked me for it today. I could have gotten fired. guess I need to start reading my emails more regularly.”