The 18-year-old American doubled a triple lutz and did not stick to his announced free programme but still managed to score 193.25 points to win the event with an overall score of 293.79 points.
Chen said he was pleased with his quads in the first half of his free programme but admitted fatigue had caught up to him and triggered mistakes.
"But this is my first grand prix win and I'm excited for the rest of the season," Chen said.
Moscow's grand prix event is the first of six to qualify for the Grand Prix Final in Japan in December, which comes two months before the start of the Winter Olympics in Pyeongchang.
Hanyu, the Olympic champion, landed three quads but missed a combination jump, tripled a quad loop and doubled a quad toeloop to earn 195.92 points in the free programme.
"I'm a little bit satisfied with my performance," Hanyu said.
"I didn't rotate my loop and I couldn't do my combination. That was the three-point difference."
Hanyu had finished second behind Chen in the short programme on Friday, earning 94.85 points after making a shaky landing on the quad loop jump at the start of his performance.
Chen was nearly six points ahead of Hanyu in the short programme, recording 100.54 points in a performance that included a dazzling quad lutz and triple toe loop combination.
Russia's Mikhail Kolyada finished third in the grand prix event with a total score of 271.06 points.
Russian pairs swept the top three places in their event, with Evgenia Tarasova and Vladimir Morozov finishing first with 224.25 points.
Tarasova and Morozov, the bronze medallists at this year's world championships, finished nearly 20 points ahead of second-place finishers Ksenia Stolbova and Fedor Klimov.
Kristina Astakhova and Alexei Rogonov finished third.
American brother and sister duo Maia and Alex Shibutani, who earned bronze at this year's world championships, won the ice dance with a total score of 189.24 points, finishing 4.50 points ahead of Russia's Ekaterina Bobrova and Dmitry Soloviev.
"It was exciting to debut our two new programmes at this competition," Maia Shibutani said. "We are very proud of the work we've put in."
(Reporting by Gabrielle Tétrault-Farber, editing by Ed Osmond)
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