"Is not I don't want to talk about my serve", Nadal said.
Tiafoe overcame a third-set blip to beat the Bulgarian No 20 seed 7-5 7-6 (8-6) 6-7 (1-7) 7-5 on Sunday and celebrated in his trademark style, screaming loudly and slapping his chest and the court in delight.
Nadal, who is aiming to become the first man in the Open era to win all 4 Slams twice if he can add to his 2009 Aussie crown, agreed Berdych had finally come to the party in the 3rd set and made life tough.
Dimitrov, meanwhile, is making his third consecutive fourth-round appearance at the Australian Open after reaching the semis in 2017 and the quarters previous year.
"I said I wasn't going to do that again", grimaced the young giant-killer, who knocked out fifth seed Kevin Anderson in the first round.
"It means the world", an emotional Tiafoe said on Eurosport.
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Bidding for an 18th Grand Slam title, second seed Nadal will now play unseeded American Frances Tiafoe for a place in the semi-finals.
American youngster Frances Tiafoe made it to the fourth round of a Grand Slam for the first time on Friday, after knocking out veteran stalwart Andreas Seppi at the Australian Open.
"I told my parents 10 years ago was going to be a pro. that I was going to do this and change their lives". "I can't believe it".
"He's super quick and he's able to change directions fast".
Tiafoe was on the front foot from the start and took the first set after 52 minutes and marked it with a one-arm raised fist salute.
"[It] always is special when you meet the opponent for the first time". An ace moved Nadal further ahead in the fifth game and the opening set was in his hands when he fired a forehand victor on Tomas' serve for a break at love and a 6-0 in just 27 minutes! "Now we're in the quarter-finals, so we'll see what happens now".
He had his chances to close out the match earlier but produced a poor third-set tie-breaker before pushing on to take the fourth set and the match in 3hr 39min.