If neither player suffers an upset, Djokovic could meet Federer in the semi-finals, with Agassi claiming to be unable to equip his pupil with a decisive tactical advantage.
"There's got to be a rule for guys who come out clearly not giving or able to give 100 percent.
Tonight was no exception", he said on the BBC.
The theory behind that setup: Players who are injured won't step on court simply to collect their prize money as an entrant, before calling it a day without finishing the match.
The quality of his play this year has been reminiscent of the peak of his career when he and the dominant golfer of the era formed a friendship as they nearly seemed to trade major tournament wins with one another. The three-time Wimbledon champion also won 72 percent of the points on his second serve, and the Serb is in a good position to go far in this tournament.
"It's a lot of money". The three-time Wimbledon champion played on the No.1 Court for the first time since losing to Sam Querrey in the third round past year.
What Djokovic was doing here, aided and abetted by a willing moderator it has to be said, was controlling the play, moving the ball about the court, dictating terms.
"It's like you wake up every day the same, and I'm happy I got through this one feeling the way I did, because in a way it's odd playing this way when you're so tense". Another win would not only put Federer in a class by himself, but extend his record number of Grand Slam championships to 19. His play, still razor-sharp and returns rapier-like in patches, can go on the blink on a whim.
"At the same time, stepping on to the same court, I try not to think about that too much and try to do what I'm supposed to do".
"I just feel that's not appropriate".
Kyrgios said he had gone against medical advice and chose to play as "it's my favourite tournament". "He's had to pull out of a lot of matches", Federer said.
On each occasion, the trainer was called to aid the two players but the treatments offered - be it massages or pain killers - could not salvage the situation. "Understanding what I'm going through and understanding that I can't always be very successful in playing in the highest possible level". "It's fine", Djokovic said.
"I guess whether that's his opinion or criticism or something else, I'm not really sure".
"Maybe a big cloud's coming in".
"If you're distracted, you're not the same player". One key to the match was Isner's inability to win any of Sela's service games in the fifth set, going 0 for 6 on break points.
"There was a letdown for the crowd". These things will surely happen, and they may even happen in the next round.
Rumours swirl around the tennis circuit - some of them are even true - but three-time victor Djokovic was in no mood to fan the flames or become entangled in a war of words.