The son of immigrants from Sierra Leone, Tiafoe got into tennis after sleeping on the floor of the training centre where his father was the head of maintenance.
Brimming with confidence after dispatching fifth seed Kevin Anderson in the second round, Tiafoe came from two sets to one down yesterday in his best ever Grand Slam run.
"For the third set, I finally showed up on the court, so that's good", said the world number 57. "I worked my a** off, man".
"I told my parents 10 years ago I was gonna be a pro tennis player and change their life", he said. "I can't believe it". That game set up the Doha finalist well to ease into the match with that forehand on the Nadal serve.
Serving at 69%, the Spaniard lost just 19 points on serve and he faced only two break points, saving them both to mount the constant pressure on the other side of the net.
The 33-year-old Berdych agreed.
The first set was a complete cakewalk for Nadal who won straight first nine games to take a 3-0 lead.
Power-packed Tiafoe squandered a break in the third and was in trouble again at 4-4, deuce until he unloaded a crosscourt forehand into the corner at deuce with such venom it nearly tore the fur from the ball.
Firing 32 winners and 17 unforced errors, Rafa did break his rival five times and that was enough for a commanding win, saving a set point at 5-6 in the third set before bringing the match home in the tie break.
"It's always special when you meet an opponent for the first time".
In his trademark post-match celebration, Tiafoe took off his t-shirt, flexed his right bicep and emulated the "Silencer" routine of basketball great LeBron James.
"It means the world", an emotional Tiafoe said on Eurosport.
He admitted he will have no chance of celebrating his birthday as he will have to prepare for the daunting prospect of facing the 17-time Spanish Grand Slam champion. "He's going to run me like insane", he said. I was going to change their life, I was going to change my life.