Either way, the extra turnout boost probably cut Mr. Cruz’s margin of victory by two points.

Mr. O’Rourke might have won with a turnout of around 10 million voters. (The actual turnout was around 8.4 million.) Without the extra edge of a Democratic wave year, it might have taken 11 million votes, a number that is not out of the question in 2020 if Texas is contested as a battleground state.

So how did Mr. O’Rourke fare so well? He did it through old-fashioned persuasion, by winning voters who had voted for Republicans and for minor-party candidates.

The results themselves make it clear that he won a lot of voters who supported Republicans in other races. He ran three points ahead of the overall Democratic state vote for the U.S. House in 2018 (adjusted for uncontested races), and ahead of every down-ballot Democrat running statewide.

Mr. O’Rourke’s personal appeal was probably a factor, and there’s no guarantee a different Democrat can replicate it. His strong favorability rating (plus-10 in the exit polls, 52 percent to 42 percent) is consistent with that possibility, though he might have also had the benefit of a relatively unpopular incumbent in Mr. Cruz. Only 50 percent of voters had a favorable impression of Mr. Cruz in the exit polls (48 percent had an unfavorable one).

But Mr. O’Rourke’s personal appeal is not the whole story. After all, many Democrats running for the U.S. House or other statewide offices posted noteworthy performances.

The tide lifting all Democratic boats in Texas was an anti-Trump rebellion.

Over all, President Trump’s approval rating was at 49 percent in the exit poll and 50 percent in the large AP/Fox Votecast poll. This is consistent with a variety of other survey data, including a recent Quinnipiac poll that put the president’s approval rating at minus-3 among registered voters in the state, 47-50. Gallup, measuring the much more diverse pool of Texan adults, put the president’s approval rating at just 41 percent in 2018.