It means Djokovic is just two wins away from overtaking Margaret Court in the all-time list of singles Grand Slam winners.
As the opening set reached its crescendo, Love Actually star Hugh Grant – sat behind Her Majesty the Queen – took a short nap in the Royal Box.
With former Prime Minister John Major also in attendance, one must wonder whether it was small talk with the 86-year-old about Downing Street dances that sent him to sleep.
Grant’s nap, however, was not an inditement on the entertainment as Cobolli and Djokovic were locked in an enthralling first set.
_(Image: PA)_ Djokovic had played the cleaner tennis – only eight unforced errors in contrast to the Italian’s 17.
Albeit Cobolli was hitting winners for fun (22 in the first set), having particular joy when seeking the corners cross court.
The seven-time Wimbledon champion did offer Cobolli quite a few opportunities at the net, though. Cobolli caught Djokovic rooted with mammoth shots into space on three occasions.
Djokovic went close to sealing the first set when he broke to lead 5-3, but he could not consolidate as a wicked forehand winner, down the line winner and Djokovic unforced error brought up three break points for Cobolli.
A fault from Djokovic was met with a strong second serve, albeit Cobolli came out on top in the exchanges. Two holds followed to force a tie-break.
In a set where there was just one point splitting the pair, it was all about moments. Cobolli found winners when he needed them most, while errors crept in at the worst time for Djokovic.
Serving first in the tie-break, Djokovic handed Cobolli the perfect start, going well deep to concede a mini break.
A pair of 134mph serves from Cobolli kept his nose in front, but a pinpoint Djokovic drop shot at the net brought the tie-break back on serve at 5-5.
However, a cross-court winner and an 137mph ace allowed the World No.24 to sweep up the first set 7-6 (8-6). Djokovic dropped his third set of the Championships.
_(Image: PA)_ Although tidy in the first, Djokovic was unrewarded for his efforts. But he kept the level of his polished display and began to make inroads.
Losing only four points on serve in the second set, Djokovic drew level in some style, making two unforced errors as he took the set 6-2 in 25 minutes.
He meant business with punishing tennis after earlier frustration. Cobolli could not buy a return.
Djokovic carried the momentum into the third, breaking in the first game before consolidating when Cobolli went on the offensive.
Attacking tennis, though, is exactly what Cobolli required to compete with the Serb. After a hold to keep the set tight, he soon earned a break of his own, capitalising on a deep forehand before finding a stunning return.
There was frustration from Djokovic, who went from winning seven successive games to losing three in a row.
He could not disguise his discontent either, tossing his racket in the air after an arduous game. Cobolli edged 4-3 ahead, although the set was still on serve.
At 5-5, a double fault from Cobolli gave Djokovic a sniff. The crowd attempted to get the underdog through the set, chanting his name.
But a deep shot when seeking a down the line winner followed but a cross court forehand dragged well wide handed Djokovic a late break.
With the Serb 30-0 up on serve and nearing his second set, Cobolli defended two big returns, but Djokovic employed the most stunning of drop shots to earn three set points. An 116mph ace was enough to wrap it up.
Cobolli knew he had to win the fourth and he was hanging in there. It was competitive and attritional. Eight games in a row went to serve.
A fatigued backhand from Cobolli caught the net and set up the break point for Djokovic. The Italian looked like he was going to come out on top until he faltered with a volley at the net which he should have dispatched.
The attention turned to Djokovic to serve for the match. After losing the first two points, Cobolli set up well to smash away. Djokovic, attempting to reach his 14th Wimbledon semi-final – the most of any man – found a stunning ace down the T to earn two match points.
Yet there was room for more drama. A massive forehand winner from the Djokovic serve kept Cobolli alive.
_(Image: PA)_ He followed it up by pushing the Serbian deep. Djokovic made the return but slipped flat on his face and Cobolli was able to put away a huge shot at the net with a slice of fortune from the net.
After Djokovic required some attention, with the referee and his opponent going to support him, he reached the semi-final soon after his blunder with a volley at the net.
“I’m feeling very fresh,” Djokovic laughs. It was a great battle today – huge congratulations to Flavio. He played on a high level; his serve surprised me a lot. He’s such a talented and skilful player, we will be seeing him much more in the future.
“Wimbledon will always be the most special tournament we have in our sport. It means the world to me that I’m still able to play in the final stages at 38-years-old.”
Djokovic will face World No 1 Jannik Sinner in the semi-final after he knocked out 10th seed Ben Shelton in straight sets.