| Venue: Flushing Meadows, New York Dates: 29 August-11 September |
| Coverage: Daily radio commentaries across BBC Sounds and the BBC Sport website and app, with selected live text commentaries and match reports on the website and app |
The Australian, who needed treatment on his left thigh after the first set, lost to the Russian.
He is into his first major semi-final.
The sixth seed plays the Norwegian fifth seed who beat the 13th seed.
A first-time Grand Slam men's singles champion will be crowned in New York on Sunday, thanks to the exit of Rafael Nadal in the last 16.
The chance to be that person still exists for Khachanov, even though he lost to Jack Draper in the third round.
When the first break point of the match went his way in the 12th game, he said he was struggling to walk.
The second set was level at one point.
The Wimbledon runner-up was frustrated when his forehand broke in the ninth game and he couldn't take any break points.
After hitting his racquet on the court, he couldn't remember the missed opportunities.
He survived two set points in the 10th game, the first when he whacked a poor drop-shot into the stands, but could not see off the Russian in the 12th.
After smashing a water bottle, which seemed to help him mentally reset in the fourth set, he took a slow-burning match into a decider with a composed tie break.
In the first game of the fifth, Khachanov took serve, superbly saved break points in his next two service games, and maintained a high level under serious pressure to win the match.
What seemed like a good chance of winning his first major was left in tatters after a furious Nick Kyrgios destroyed two racquets.
He wants to win his first major title and become the new world number one.
Having the top ranking on the line is providing extra motivation for the young man who lost to Nadal in the French Open final.
If he makes the final, he has a chance of pipping Nadal to the title. The winner of the trophy would become the world's top ranked person.
"I didn't know I could be number one when I began this tournament," said the man. Young players think about that.
It's a bit of motivation to keep going. I can leave New York as the world's top ranked person.
I don't want to pay too much attention to it.
The roof was wet in New York. After Berrettini fought back to 4-5, he took the first set with ease and went up 6-1 in the second.
The Italian broke early in the third set but couldn't convert two set points and lost the set.
He won a tie-break after breaking back to reach his second Grand Slam semi- final.
Berrettini was at a loss to explain his poor start to the game.
He did not know what happened. I played a bad match and he played a good one.
The worst day of the tournament was probably the most important one. I felt like I wasn't playing well. I was not feeling like myself. I believe he was doing well.
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