Russian showed a score of 90.86 points.
American Jason Brown (96.41) leads after the short program, and his compatriot Nathan Chen (86.94) closes the top three.
Another Russian athlete, Dmitry Aliev, is in ninth place (75.15).
Free skaters will present the program on November 24.
Earlier, Zagitova refused to answer whether she wanted to meet with Medvedeva in the final of the Grand Prix in Vancouver.