Hoy rode in the first of three Keirin heats and had to finish in the top two to advance at the first time of asking.
The world Keirin champion clearly did not wish to hang around and followed Njisane Nicholas Phillip's early move before powering to the front with one and a half laps to go.
The 36-year-old eased over the line, with Simon van Velthooven the only rider who could go with him as the New Zealander also advanced at the first time of asking.
Hoy took his Olympic gold medal-winning tally to five on Thursday with victory in the Team Sprint.
Sarah Hammer of the United States leads the women's Omnium by one point from Great Britain's Laura Trott, after four of the six disciplines.
Hammer finished the 3km Individual Pursuit quickest in 3:29.554, with world Omnium champion Trott second in 3:30.547.
Pendleton, who is set to retire after today's competition, won Keirin gold on Friday and was today seeking a third Olympic title in all to become Britain's most successful female athlete.