Roswell, who won a team pursuit gold at London 2012, beat Australian Annette Edmondson by more than three seconds with a time of three minutes 31.
The 26-year-old Kenny, a triple Olympic sprint champion, lost 2-1 in the three-race final to the powerful New Zealander Sam Webster in a cat and mouse race at the Chris Hoy Velodrome.
It was his second Games silver, the other coming in the team pursuit on Thursday.
“It’s difficult for anything to surpass the London 2012 Games,” individual pursuit world champion Roswell told Reuters.
“But this is really special because it was an individual medal which I didn’t have a chance to do at the Olympics after the event was taken out after Beijing 2008.”
The 25-year-old also set a new Games record with a ride of three minutes 29.038 seconds on her way to the final.
“To do a new Games record on this track is absolutely incredible,” said Roswell.
“It’s a new personal best for me by over a second and to go sub 3:30 is quite a nice psychological barrier to break especially in qualifying because you know you’ve got that gap over everybody else.”
Roswell goes in search of another gold medal in the 10-km scratch race final on Saturday.
Home favourite Katie Archibald narrowly missed out on the bronze for Scotland, losing out to Australia’s Amy Cure.
Cure’s compatriots, Jack Bobridge and world champion Alex Edmondson, were involved in a duel for the 4,000 pursuit and it was the former who snatched gold.
Bobridge came out of retirement to be at the Games and his decision was vindicated, retaining the title he won in Delhi in 2010.
Marc Ryan of New Zealand took bronze.
(Editing by Tony Goodson)