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I know that the great Judit Polgar defeated Kasparov, but he was no longer World Champion at that point. She defeated Anand, but he was not yet World Champion at that point. She defeated Kasimdzhanov, but his championship wasn't undisputed because of the FIDE-PCA split. And so on.
Has a woman ever defeated a reigning undisputed World Chess Champion in classical chess?
Sorry, but the answer is "no".
I used ChessBase and the Mega 2020 database to search various combinations of players, focusing primarily on Women's World Champions, Judit Polgar, Hou Yifan, Vera Menchik from the 1920's and 1930's, Lyudmila Rudenko, Elisaveta Bykova, Olga Rubtsova, Nona Gaprindashvili, and Maia Chiburdanidze. I stopped after Maia Chiburdanidze with the exception of Polgar and Yifan since I would have remembered a victory by the more recent Women's World Champions starting with Xie Jun next. With the exception of Vera Menchik, who played Capablanca a number of games, none of the old Soviet women ever played any of the world champions.
Given that you were looking for a defeat of a sitting world champion in classical, no woman has ever done that yet.
The only ones to ever beat men, who already had been world champions, were Judit Polgar's victories over Karpov in classical at Hoogeveen in 2003, and Chorus in 2003, and the Champions League in 2007 (still the only victories by any woman in classical over even a former World Champion), and 8 wins in rapid, and a few blitz. Also, she beat Kasparov in rapid at the World Rapid Championship in 2002. She also had one rapid victory over Magnus Carlsen in 2012 in Mexico City, but that was a year before he won the title.
Hou Yifan had two wins over Kramnik at the Media Kings Rapid in 2016. She also has had some victories in blitz.
After a bunch of back-and-forth comments below, I was asked to add my methodology to the answer, which I agreed to do. I do not claim my answer to be worthy of a scientific study and the scrutiny that would be associated with it. I was just trying to give a reasonably educated answer to the question. Whether I missed a rapid game against a former World Champion in my list, that is possible, but that was also just supplemental information I provided, and was not really part of the answer to the OP’s question since the question was officially only about classical chess. I would also take classical chess to mean over-the-board in a tournament since for it to mean anything, it had to be serious chess (this is not to be confused with relays of OTB tournaments, where the games are not really being played on the Internet).
First, it is important to understand that if no woman has ever beaten a sitting World Champion in classical chess, it would be asking to prove a negative, so you can always some up with a “what if” situation that I did not search for. I had to draw the line somewhere, and I drew the line based on my searches of the best women players of their times (and all the world champions of their eras they may have faced), my fairly extensive knowledge of chess history, and 40 years of reading MANY sources on a once monthly (before the Internet, when all I was “Chess Life” and “New in Chess” magazine), and since the Internet, I read an average of three sites per day, every day (currently chessbase.com, chess.com, and chess24.com, and twic and chessninja in the past).
It is also important to know, and this is where the history comes in, that the best women of the generations prior to the Polgar sisters, were MUCH weaker, often only in the 2300-2400 range, but it was also before the ELO system existed, so that is an estimate. I also know that back then, men simply did not play women virtually at all…Vera Menchik was the exception.
All of the major advances in women’s chess strength to the Grandmaster level have come during my lifetime, when I was active playing, and actively reading the sources I referenced above, so I also ask for a little common sense: This would have been HUGE news, as was Polgar beat Kasparov in RAPID. I cannot find anything on Google about a woman beating a sitting World Champion in classical chess. I would not have missed it.
Lastly, World Champions since Fischer have been 2700+, and there are only two women, who reasonably have had a shot at beating a World Champion in classical, and a lot of that is due to opportunity and invitations to elite events: Judit Polgar, and Hou Yifan, so you really do not have to look much further than their games, which limits the searching a lot.
This answer is mainly intended as an exposition of PhishMaster's answer, which I'm confident is correct, if we treat the OP as only including serious games (this excludes random games on the internet which nobody recorded the moves of).
In recorded chess history, men have been significantly stronger than women. The gap is usually quite large, for example as of time of writing the highest-rated male chess player is World Champion Magnus Carlsen at 2862 rating, while the highest-rated female chess player is Hou Yifan at 2664. This is an elo gap of 198 points, which means that in a match between the two, Carlsen is expected to score about 76/100.* The gap is very large, so much so that top invitationals usually have only male players. It's not that the organizers don't want to invite women, but rather that any woman participating would very likely be a metaphorical punching bag.
In recorded chess history, there are three exceptions to the above - women of exceptional strength whom tournament organizers are happy to invite. If you imagine all female chess players' rating as a Bell curve, these women would be way out in the extremes. The three are:
Accordingly, if one is going to look for wins by a woman over a male world champion, one would start by examining the games of these three players. The fact that none of them beat a reigning world champion at classical time controls makes it pretty damn likely that no woman has ever done it, and I would be prepared to metaphorically eat my hat if someone can find a counterexample.
That said, Vera Menchik, Judit Polgar and Hou Yifan have all beaten top-class grandmasters. Vera Menchik won these two games against future world champion Max Euwe. These games were played in 1930-1931, four years before Euwe became world champion, and at a time when he was one of the most credible challengers for the championship. Judit Polgar won this game against future world champion Viswanathan Anand in 1999, when Anand was ranked #2 in the world. Finally, Hou Yifan has defeated Fabiano Caruana in 2017. Caruana has never been world champion, but he was (current champion) Carlsen's opponent in the 2018 match, and that match ended drawn.
tl; dr: no woman has yet beaten a reigning undisputed world chess champion in a serious game, under classical time controls - but some have come close.
*In chess, a win is worth 1 point, a draw is worth 1/2 points, and a loss is worth 0. An example of how the score could reach 76/100 is if Carlsen wins 52 times and the remaining 48 games are drawn.
**Usually the world championship is decided in one-on-one match play. During this period in which Judit Polgar played in the world championship, there was some turmoil in the chess world and FIDE (the organizing body of chess) experimented with other formats, such as the 8-player double round robin Judit played in. There were also 128-player knockout world championships, which because of their size & format (knockouts are by nature more random) are much less prestigious.
Another woman to add to the list of close, but not quite, is Pia Cramling.
Never in Classical. It's almost never happened across all time controls. The only two examples I can find are actually from the same tournament - 2009 World Blitz Championship. Both Judit Polgar and Alexandra Kosteniuk beat Anand (Kosteniuk also beat Magnus in this tournament). Anand still finished second just below Carlsen, and the women finished in the bottom 4 of the tournament, but you can see the brilliancy in those games.
