First Skinner broke the Olympic record with a time of 9.703, before last man off, world champion Jason Kenny obliterated the field and set a new Olympic mark of 9.551 seconds.
Both riders are on a roll, having been part of GB's gold-medal-winning team sprint line-up along with Philip Hindes. The trio set a new Olympic record in that discipline on Thursday.
Matthew Glaetzer (Australia) qualified third fastest, with Denis Dmitriev (Russia) in fourth.
The top 18 riders out of the 27 starters will now progress to the 1/16 finals, which take place later on Friday night. Further rounds take place on Saturday, and the finals will take place on Sunday.
Rio 2016 Olympic Games, men's sprint qualifying
1. Jason Kenny (GBR) 9.551 [Olympic record]
2. Callum Skinner (GBR) 9.703
3. Matthew Glaetzer (AUS) 9.704
4. Denis Dmitriev (RUS) 9.774
5. Gregory Bauge (FRA) 9.807
6. Nijsane Phillip (TTO) 9.813
7. Damian Zielinski (POL) 9.823
8. Jeffrey Hoogland (NED) 9.837
9. Sam Webster (NZL) 9.880
10. Edward Dawkins (NZL) 9.895
11. Francois Pervis (FRA) 9.898
12. Joachim Eilers (GER) 9.908
13. Chao Xu (CHN) 9.939
14. Pavel Kelemen (CZE) 9.969
15. Rafal Sarnecki (POL) 9.980
16. Fabian Hernando Puerta Zapata (COL) 9.981
17. Patrick Constable (AUS) 10.010
18. Maximilian Levy (GER) 10.035
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