Yee, who improved on the silver he won at the Tokyo Olympics three years ago, caught great rival Wilde on one of the last corners of the concluding 10-kilometre run, with the New Zealander finishing second and France's Leo Bergere winning the battle for third.
Yee's huge smile on the medals podium showed how much the gold meant to him after he upgraded on second place in Tokyo.
The women's triathlon took place just before the men's in a huge relief for organisers after the River Seine had failed pollution tests on previous days.
France's Cassandre Beaugrand took an emotional gold in that event with Beth Potter of Britain winning the bronze.
Yee followed a rich British tradition in the Olympic men's triathlon after Alistair Brownlee took the title at the 2012 London Games and in Rio four years later.
His brother Jonathan Brownlee also took the silver medal in London.
