Chen, at his first Olympics, showed consistency throughout his dives, gaining high scores to total 585.30 with his tight spins and clean entries into the water even as his rivals, including team mate Qiu Bo, stumbled.
Boudia, who won gold in London, recovered from a poor semi-final performance, where he finished 10th, to acquire 525.25 points. His final, lower-scoring dive pushed him down to third position at the last minute behind Sanchez who scored 532.70.
Image credit: AFP
Daley qualifies in style for 10m platform final
London 2012 silver medallist Qiu, ended the competition in fifth place despite scoring a perfect 10 from all six judges on his third dive, after low scores of 47.25 and 47.50 on his second and fifth attempts knocked him out of the running for a podium spot.
Great Britain star Tom Daley, who had been expected to be a strong medal contender, was surprisingly ousted in the semi-finals after he botched three of his six dives to come in last. He had topped the preliminaries on Friday.
[BEST TWEETS: Daley crashes out and his fans struggle to cope]
The only gold China failed to win in Rio was in the men's 3 metre springboard event where they took the bronze instead.
China's Ren, 15, takes gold on 10m platform
Jack Laugher wins diving silver for his second medal of the Games