The British duo, who also took gold along with team-mates Neah Evans and Ellie Dickinson in the women’s team pursuit, thrilled the London crowd with a dominant victory.
In a final interrupted by a crash eliminating Russia and the United States, Kenny and Archibald looked in control from the off.
A blistering finish from four-time Olympic champion Kenny secured top spot ahead of Australia, with Belgium taking bronze.
Matt Walls also won gold for Britain, in the men’s omnium.
A strong ride from the 20-year-old from Oldham saw him triumph in a points race in which the lead changed hands several times.
Walls claimed gold with 131 points, with Mexican Ignacio Prado Juarez second on 123 and Italian Elia Viviani third with 114.
Victory completed a full set of medals for Walls after he won bronze in the team pursuit and Madison silver alongside Fred Wright.
The inexperienced British duo – aged just 19 and 20 – scored in seven of the 12 sprints and finished strongly to hold off third-placed Spain.
Walls said: “It was a really hard race, and the standard of the field was mad – there were so many good riders.
“We got quite a few points at the end, so we’re really happy to come away with silver.”
There was disappointment in the men’s keirin where Jack Carlin was edged out of the medals into fourth position, and the women’s omnium in which Elinor Barker finished fifth.
Archibald reached the quarter-finals of the women’s sprint where she was beaten by the eventual winner Stephanie Morton of Australia.
In-form Huddersfield cyclo-cross racer Matthew Taylor took over at the top of the Kinesis Yorkshire Points Series when he stormed to victory in round nine of the series at Thornes Park in Wakefield yesterday.
The newly-crowned North of England champion, Taylor’s victory in Sunday’s race was his eighth victory in as many rides, and saw him go to the top of the standings with maximum points in the senior category.
Taylor was quick out of the blocks on lap one alongside promising junior rider Jenson Young, the Oldfield-Paul Milnes Cycles rider from Barnsley, while JLT Condor pro Graham Briggs from Doncaster and Shibden CC’s junior Joe Coukham were not far behind.
But Taylor hit out on lap two and extended his lead, crossing the line 19 seconds clear of Young, who held off Briggs who settled for third, another 55 seconds behind Young.
In other categories there was another win for Alison Kinloch (PH MAS Paul Milnes Cycles) in the women’s race.
Her time of 46.15 was 19 seconds clear of team-mate Lily Greenhalgh (PH MAS Paul Milnes), while Libby Greatorex (Cyclocross Rider) was another 1.15 behind in third spot. Ian Taylor (C and N Cycles) was the fastest veteran, holding off Zepnat RT’s former over-50s national champion Tim Gould to the line.
In the youth race Holmfirth CC rider Oliver Akers was victorious by just six seconds from East Bradford CC’s Ben Ramsden, while Tom Scott (Holmfirth CC) was third and Imogen Wolff (Holmfirth CC) was the fastest girl.