Skating to "Parisian Walkways," Hanyu opened with a quad toe-loop and hit all his other jumps to the delight of a sellout crowd at Marine Messe. His 99.84 points surpassed the previous high of 98.52 by Chan at the Trophee Bompard last month.
"I was surprised when I saw the score," Hanyu said. "All my jumps were very good. I lost a bit of concentration near the end and need to improve that but now I have to focus on the free skate."
Chan hit his opening quad toe-loop, triple toe-loop combination but touched the ice on the landing of his triple axel and doubled a planned triple lutz to finish with 87.47.
"I'm not super happy with how I skated," Chan said. "When you achieve close to perfection like I did in Paris it's hard to do it again. Tomorrow is a new day and the long program is where it's won and where it's lost so we'll see."
Nobunari Oda, a late substitute for injured Japanese compatriot Daisuke Takahashi, finished third with 80.94.
Mao Asada led after the women's short program with 72.36 points despite under-rotating her opening triple axel.
"The judges saw it as under-rotated but I personally felt good about it," Asada said. "So I won't be worried about it going into the long program."
Adelina Sotnikova, one of four Russian skaters in the field, was second with 68.38 followed by Ashley Wagner of the United States who had 68.14.
The GP Final is the first and only event where most of the world's top skaters will meet before the Sochi Olympics. The men's free skate and the ice dance short program are scheduled for Friday.