Britain were defending women’s madison champions coming into the 120-lap race, with Katie Archibald and Dame Laura Kenny having won the inaugural Olympic race three years ago in Tokyo.
GB were the only team on the podium to not take a 20-point lap, with bronze medallists the Netherlands the first to make the catch.
With sprints taking place every 10 laps, Barker and Evans – who are the world champions – made the perfect start by taking the opening five points on offer.
They remained in the medal positions throughout, though that looked in danger when first the Dutch then Italy lapped the rest of the field, with the American duo often in touching distance of the British pair.
Barker and Evans took the most points of any nation on the sprints, with Barker – who has a team pursuit Olympic medal of every colour after winning bronze earlier in the week – launching a fierce attack to wrap up the double points on the last 250m.
“We really, really wanted gold,” Barker – a four-time Olympic medallist at 29 – told BBC Sport.
“We came in as world champions which obviously meant we put that pressure on ourselves. We had a target on our back potentially.
“We said it wouldn’t change the way that we raced but it was hard not to feel like we needed to take responsibility for things at times and perhaps that’s what we’ll pick up in our analysis but also I think – an Olympic medal.
“There are plenty of world champions this week that haven’t medalled. I think every single medal is a huge achievement.”
Their silver medal marks a redemption for the pair, who crashed out of the madison at January’s European Championships.
“We actually stuck to the plan pretty well,” said Evans, 34.
“The thing with madison is that it is so unpredictable. [Europeans] we went in as favourites and did the first bit and crashed.
“To come away with a medal is huge because there’s nothing guaranteed. It’s unorganised chaos. You’re like if only… but it’s an Olympic silver medal.”
Elsewhere in Friday’s action, Emma Finucane and Sophie Capewell – who were crowned team sprint Olympic champions alongside Katy Marchant on Monday – progressed to the 1/8 finals in the individual sprint.
That event continues on Saturday, when the men’s keirin also gets under way and Ethan Hayter and Ollie Wood contest the men’s madison.
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