Djokovic looks highly likely to be waiting for Thiem in the final if the Austrian can get that far and he will be eyeing his chance after taking out the 2014 champion Cilic.
“I am much happier, not 100 per cent yet, I still have to raise my level if I want to go deeper, especially in the next round,” Thiem said of his game.
“Normally I am capable of doing this in the slams. I am not 100 per cent happy with the way I am playing yet. Today was a good win against a great champion and a good player and that should give me a boost.”
Next up for the Austrian is Felix Auger-Aliassime, who continues to look imperious, and it is a tantalising clash.
The 15th seed, still only 20, trounced Corentin Moutet 6-1 6-0 6-3 to record his best ever performance in a grand slam.
Auger-Aliassime may still be baby-faced but he is determined to show a killer instinct on court.
“I’m here to impose myself,” he said. “Outside the court I’m a pretty kind person but once I step on court, it’s the best man that wins.
“Only one survives. You’ve got to step it up with that animal and killer instinct.”
Third seed Daniil Medvedev also continued his cruise through to the fourth round.
The Russian’s run to the final last year was full of drama but so far he has not lost more than four games in any set across three matches and was in complete control in a 6-3 6-3 6-2 win over American JJ Wolf.
Medvedev is among the 10 players who are subject to extra measures after being identified as having been close to Benoit Paire prior to his positive test for Covid-19.
The seven who had prolonged contact have now been ordered to quarantine in their rooms following intervention from public health officials, but Medvedev, one of the other three, revealed his restrictions have not changed.
He said: “I actually had no contact with Benoit. I don’t know how they check it. I think it’s by credential, and maybe I was in the same room with him.
“So, after talking to USTA (the United States Tennis Association) and a doctor from the New York department, I think, they said, ‘OK, just do a test every day and you live normal. If we can call this normal.
“I have done maybe five tests, five negative tests, and I will continue to do them every day. It doesn’t bother me at all.”
Medvedev will next face another American Frances Tiafoe, following the latter’s straight sets win over Marton Fucsovics.
Tenth seed Andrey Rublev has been nearly as impressive as his fellow Russian Medvedev and he needed just an hour and 24 minutes to defeat Italian Salvatore Caruso 6-0 6-4 6-0.
Canadian Vasek Pospisil began the tournament by helping Novak Djokovic set up the Professional Tennis Players Association but off-court distractions appear to have galvanised him, and the 30-year-old reached the fourth round here for the first time with a 7-5 2-6 4-6 6-3 6-2 upset of eighth seed Roberto Bautista Agut.
Sixth seed Matteo Berrettini, a semi-finalist last year, is going well again, beating Casper Ruud 6-4 6-4 6-2, while young Australian Alex De Minaur recovered from losing the second set to love to beat 11th seed Karen Khachanov 6-4 0-6 4-6 6-3 6-1.