The mentality of just one more to win it all is the easiest to exploit. That's literally your opponent letting down their guard. Think of it as them prematurely celebrating internally in oder to cool their own nerves. Basically a form of self hypnosis. This self hypnosis however can also slow down their reaction speed and cause them to make bad plays.
Each match/point you win at that point will half your opponent(s) moral and obliterate their momentum. Win a few and you'll have the win in the bag... unless you start thinking "just one more..."
The idea is basically to stay serious till the end. No mercy and never give up.