Down 3-5, Federer challenged a Berdych serve but was unable to survey the evidence due to a faulty hawk-eye video display.
Advised that the call had gone against him and he had lost his last remaining challenge, Federer admonished chair umpire Fergus Murphy in a rare display of annoyance from the ice-cool veteran.
"You can't steal my challenge now," Federer told the official.
"Are you comfortable with this? Are you okay with it? You can say 'OK, he's already been screwed over once; you don't want it to happen twice in a row'.
"It's your call; you're the umpire."
The incident appeared to light a fire under Federer, who won four of the next five games and saved a set point before storming through a tiebreak to take the first set.
Running Berdych ragged with some of his best shot-making of the tournament, Federer smashed 61 winners - almost three times as many as his opponent - and won 23 points at the net.
"I hung around. Had to get a bit lucky, a bit angry, a bit frustrated maybe at the umpire," Federer said.
"I actually thought the call was good and probably he was right taking the (challenge) away ... I was just a little bit frustrated."
Federer admitted Berdych's hot start had left him feeling the heat and in search of a different strategy.
"I tried to play a bit more aggressive, get some rhythm going, because Tomas found that early," he said.
"That's why I was under pressure.
"Coming back from 5-2 in the first set, it was clearly big tonight."
A dejected Berdych took little consolation from his admirable fighting effort.
"I played a good match, but I didn't play my best," he said.
"When I played my best, I was able to beat him. That's not what happened today."
Federer's third-round demolition of Berdych last year, on the comeback from injury, proved to be a defining moment on his way towards an odds-defying fifth Australian Open triumph.
If the same is to be true this year, Federer will need to get past a dangerous opponent in Chung in their first career meeting.
"He reminds me a lot of Novak (Djokovic) the way he goes forward and backwards," Federer said.
"I"m keen to play against him. He has nothing to lose.
"I will tell myself the same and see what happens."