It has not always been the case that more educated voters tend to vote for Democrats. This really only started to be case in 1992 when Bill Clinton won his first Presidential election in a dramatic shift of educated voters from the Republican to the Democratic party (whose respective left-right leanings have been a moving target in the post-World War II political era).
For example, in the era of New York Governor and Vice President Nelson Rockefeller and President Gerald Ford, in the 1960s and 1970s, educated voters decisively favored Republicans and the Republican party was much more moderate on social issues. (For what it is worth Gary Trudeau's comic strip Doonsbury provides a detailed contemporaneous social history of the process of this shift in the respective major political party's coalitions and policies in a very intimate way.)
The tendency of more educated votes to vote for Democrats is a relatively recent development that flows from the declining political salience of economic issues relative to cultural issues for many voters.
But, for evidence that it is real, consider, for example, an analysis of exit polls from the 2016 Presidential election prepared by the 538 blog. It begins:
Sometimes statistical analysis is tricky, and sometimes a finding just
jumps off the page. Here’s one example of the latter.
I took a list of all 981 U.S. counties with 50,000 or more people
and sorted it by the share of the population that had completed at
least a four-year college degree. Hillary Clinton improved on
President Obama’s 2012 performance in 48 of the country’s 50
most-well-educated counties. And on average, she improved on Obama’s
margin of victory in these countries by almost 9 percentage points,
even though Obama had done pretty well in them to begin with.
It continues, much later on, to state with regard to the least-well-educated counties:
Clinton lost ground relative to Obama in 47 of the 50 counties — she
did an average of 11 percentage points worse, in fact. These are
really the places that won Donald Trump the presidency, especially
given that a fair number of them are in swing states such as Ohio and
North Carolina. He improved on Mitt Romney’s margin by more than 30
points (!) in Ashtabula County, Ohio, for example, an industrial
county along Lake Erie that hadn’t voted Republican since 1984.
Further analysis rejects the hypothesis that income rather than education is involved. The implication of this fact is that the political identity of voters in 2016 and other recent elections where education has been a more important factor than income in predicting electoral preferences is more more cultural than economic.
The Pew Research Center tracks the trend back to 1980:
As the chart shows, the really decisive shift in the partisan leanings of college educated voters took place between 1988 Presidential election (won by George Herbert Walker Bush) and 1992 (won by Bill Clinton) and has changed only modestly since then.