Yes booking flights is often much cheaper when you book the flight last minute.
The airline is willing to give you a good deal on last minute flight tickets so that they fill empty seats and they do know that a lot of business travelers that fly need to and tend to book flights at the last minute.
So if you want the best deal on cheap airline tickets it's better to book the flight the last minute to get the cheapest flight tickets.
However sometimes you may need to book a flight beforehand and may need to pay a higher price for your airline ticket.
But sometimes you can even get good deals when booking the the flight and airline tickets before the flight.
You can get good deals on airline tickets through Google Flights or Even Kayak where they have good deals and help you book a cheap flight.