Hanyu racked up 87.65 points to lead after the first day, with China’s Yan Han in second with 85.08, and Richard Dornbush of the USA in third with 83.01 on the board.
Takahashi, who has announced he will retire after the Sochi Winter Olympics, was fourth on 82.62 after a disappointing performance to Beethoven’s "Moonlight Sonata".
Hanyu thrived as he skated to "Parisian Walkways", but he still managed to highlight a blemish in his performance.
“I don’t know the reason I popped the lutz,” Hanyu said. “But I felt I did really well otherwise and put myself in a great position for tomorrow’s free skate.”
In the ice dance short programme, Tessa Virtue and Scott Moir took the lead with a score of 75.12.
Meanwhile, Meagan Duhamel and Eric Radford of Canada grabbed the top spot in the pairs with 70.44.
The women’s skate, featuring two-time world champion Mao Asada, gets under way on Saturday.
Men's short programme results
1. Yuzuru Hanyu (Japan) 87.65
2. Yan Han (China) 85.08
3. Richard Dornbush (U.S.) 83.01
4. Daisuke Takahashi (Japan) 82.62
5. Song Nan (China) 81.16
6. Kevin Reynolds (Canada) 78.34
7. Denis Ten (Kazakhstan) 78.05
8. Takahito Mura (Japan) 78.03
9. Ross Miner (U.S.) 74.01
10. Max Aaron (U.S.) 72.46