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I'm curious whether women's suffrage has ever changed the direction of an election. Polls often show differences between men and women, but they are often fairly highly correlated, so I wonder if women's suffrage has ever proved decisive in an election.

Since this is a matter of curiosity I'd welcome responses from anywhere in the world; or for more narrow focus: federal and gubernatorial elections in the United States following the adoption of the 19th amendment in 1920.

(The question is not whether or not women's suffrage confers political power on women. Candidates have to appeal to the populace long before the final election, and suffrage certainly affects that political calculus.)

You're not the first person to ask this question.

It's obviously not possible to know exactly how any election would have gone in things were different, but we have enough demographic polling data to make educated guesses.

FiveThirtyEight has done extensive analyses on what voting maps would look like if only specific demographics voted. In this most recent midterm they estimated/predicted that an all male electorate would have elected a majority Republican House of Representatives.

I find this an unsatisfactory answer but perhaps it will provoke someone to make a better one along similar lines. In the 2012 US presidential election, men voted (according to exit polls) 52:45 in favour of Romney over Obama, compared with the overall result of 51:47 in favour of Obama.

So if we assume the exit polls give a perfectly accurate indication of actual voting patterns, going from the whole electorate to just men turns Obama+4 into Romney+7, an 11-point swing. And if we assume that that translates into an 11-point swing in every state, that gets Romney at least these states listed on the Wikipedia page about the election as having <10% margins for Obama: Florida (1%; 29EV), Ohio (3%; 18EV), Virginia (4%; 13EV), Colorado (5%; 9EV), Pennsylvania (5%; 20EV), New Hampshire (6%; 4EV), Iowa (6%; 6EV), Nevada (7%; 6EV), Wisconsin (7%; 10EV), Minnesota (8%; 10EV), Maine-2 (9%; 1EV), Michigan (10%; 16EV). Since Obama won by 332:206 EV, a margin of 126 EV, transferring 64 EV from Obama to Romney would yield a Romney win. The actual total of the numbers above is 142.

Those italicized assumptions are pretty dubious, but it seems like there's probably enough slack to make it not matter: a uniform 5.4% swing would have got Romney the states of Florida, Ohio, Virginia, Colorado and Pennsylvania, already comfortably more than enough to win.

To do this analysis properly we'd need state-by-state exit poll data broken down by sex (which may well exist but my very cursory search didn't find it), and estimates of how accurate exit polls are (which may also exist but I confess I haven't looked), and enough effort to put those things together properly (which, as you can see, I haven't provided) -- which is why I am not altogether satisfied by this answer. It is, however, enough to convince me pretty firmly that if women's votes had been removed from the 2012 US presidential election (while somehow changing nothing else) then Romney would have won it instead of Obama.

In the 1933 Spanish general election women were enfranchised by the first time, and the right won the election - while in the previous 1931 election the left had won. One of the cited causes of that victory of the right was that women were more influenced by the Church than men, so they tended to follow more their priest's advice and vote for conservative parties.

Ironically, the enfranchisement of women that helped the right to win had been championed by the left and opposed by the right.

Addition (source and limits of the answer):

As the answer says, enfranchisement of women has been cited as one of the causes of the victory of the right - and that has been often repeated. However, as several comments point, how big was its contribution even whether there actually was a contribution is not clear, and even if it were it would be difficult to prove.

Just to give a synthesis - not very different from the Wikipedia article cited in comments -, I cite Gatell, Cristina. "Dones d'ahir, dones d'avui" Barcelona, 1993. ISBN:84-7533-835-6 page 63:

S'ha especulat molt sobre el sentit del vot femení en aquestes eleccions i la premsa d'esquerres va atribuir la victòria de les dretes al vot de les dones. Estudis posteriors han posat seriosament en dubte la vella creença del vot conservador de les dones i han demostrat que no existeix una correlació directa entre nombre de dones al cens i vots a la dreta.

A tentative translation:

There has been a lot of speculation about the meaning of female voting in these elections and the leftist press attributed the victory of women's right to vote. Further studies have seriously undermined the old belief in the conservative vote of women and have shown that there is no direct correlation between number of women in the census and votes on the right.

Although the explanation of the election outcome according to female vote is plausible, it should be noted that for leftist press this explanation could be a way to save face, because any other explanation would have need to blame at some extent the leftist government. Interestingly, I also checked a book of contemporary articles of right leaning Carles Sentís and in his very short summary of the causes of the outcome, the vote of women isn't mentioned - some actions of the government are mentioned, instead.

I might suggest the election of Susanna Madora Salter as mayor of Argonia, Kansas, in 1887.

From the Kansas Historical Society page on her:

First woman mayor in the U.S...

Soon after Kansas women gained the right to vote in municipal elections, voters elected (Salter)...

(She was) Nominated on the Prohibition Party ticket by several Argonia men as a joke, Salter surprised the group and received two-thirds of the votes.

A cursory glance at the data available doesn't lead me to a 'smoking gun', but the circumstances surrounding the election -- nominated 'as a joke' and elected 'just weeks after Kansas women had gained the right to vote in city elections' -- leads me to think it could be a good candidate for further research.