He's just the second man ever to reach 10 or more semifinals in Paris, after Rafael Nadal, who's in his 13th this year. The two could meet in the final on Sunday, should they win their semifinals Friday.
Things looked dicey for Djokovic early on in the match—visibly struggling with a neck injury, he not only dropped the first set, he faced double break point serving at 1-all, 15-40 in the second set.
But that's when the match turned. Djokovic won eight of the next nine games to take the second set and build a 3-0 lead in the third—Carreno Busta took the next three games to tie things up in the third at 3-all, but Djokovic bounced back with three games of his own for a two-sets-to-one lead.
Djokovic snuck out the only break of the fourth set for a 4-3 lead and the two players held from there until it was all over, the Serb ripping a perfectly-angled crosscourt forehand winner on match point.
Carreno Busta's winners-to-unforced errors differential for the match was better than Djokovic's—the Spaniard was +13 (42 to 29) while the Serb was +12 (53 to 41). But Djokovic got much, much better as the match went on, going -9 in the first set (7 to 16) but +21 over the last three sets (46 to 25).
"I definitely didn't feel great coming into the court today," he said in his post-match press conference. "Few things happened in the warm-up. I had to deal with those issues coming onto the court. As the match went on, I felt better, didn't feel as much pain. But I don't want to take away anything from his good performance. Especially for the first set and a half he was the better player, dictating the play.
"It took me about a set and a half to really get comfortable and start playing the way I should."
The 2016 Roland Garros champion was also asked to detail exactly what the injury was.
"I had some neck issues and some shoulder issues. I'll just say that," he said. "I mean, I don't want to get really too much into it. Obviously I'm still in the tournament, so I don't want to reveal too much.
"I'm feeling okay. I think, as I said, as the match progressed, I warmed up my body, and the pain kind of faded away. It allowed me to play better and better, and feel better."
It was the pair's first encounter since their fourth-round match at the US Open 31 days earlier, when the Serb was defaulted late in the first set for accidentally striking a lineswoman with a ball. It was also Djokovic's 39th win in his last 40 matches since last November, the only loss being the default.
Djokovic isn't just through to his 10th career semifinal at Roland Garros, he's now into his 38th career semifinal at a Grand Slam, the second-most for a man all-time, after Roger Federer, who's reached 46.
He was asked about his continued success at the majors in his on-court interview with Marion Bartoli.
"Well, many players have said it before me, but these four tournaments—the four Grand Slams—matter the most, probably, in the tennis history," he said. "They're the most popular tennis events in the world. A lot of kids, when they take the racquet in their hands, they dream of winning Roland Garros, Wimbledon, the Australian Open and US Open. I've been very fortunate to play well throughout my career in Grand Slams, and I value them as the biggest priority. I'm very proud of this achievement."
Up next for the No. 1 seed will be No. 5 seed Stefanos Tsitsipas, a 7-5, 6-3, 6-2 winner over No. 13 seed Andrey Rublev earlier in the day. Djokovic is 3-2 against Tsitsipas, winning their only clay-court meeting in the final of Madrid last year, 6-3, 6-4. The two have never met at a Grand Slam.
"I expect a really tough, tough match, tough challenge for both of us, Djokovic said. "Semifinals of a Grand Slam, this is what you expect. You expect to play a Top 5, Top 10 player. This is what I get.
"I'm hopefully going to be able to feel my best and play my best."