It was her first individual title in an event that has now been won by U.S. swimmers in three successive world championships.
France's Aurelie Muller, who defended her 2015 title in the 10km on Sunday, took silver and Brazil's Ana Marcela Cunha the bronze - her eighth world championships open water medal.
Twichell, who won gold in the five km mixed team event in the 2011 championships and individual bronze, touched out in 59 minutes and seven seconds after swimming a tactical race and making a break at the start of the second lap at Lake Balaton.
Muller was 3.5 seconds slower.
"We swam at a perfect pace, and I left the others at the right moment close to the end," said the American.
"My shoulder needed icing after the competition, but it had been injured before and I have had some problems with it for a couple of years."
American Haley Anderson, winner at the past two world championships, finished fifth.
(Reporting by Alan Baldwin in London, editing by Christian Radnedge)
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