Riding for Team USN, the trio qualified for the final in third place with a personal best before they bettered that effort in the final to claim bronze.
Their time of 3:24.419 was enough to edge out Italy from the medals, but not Canada and Ukraine who topped the podium.
“The girls rode a lot better in the final, improving technically,” coach Darren Tudor said. “We learnt a lot from the first ride and slightly changed our tactics.
“This worked for the girls and they secured a comfortable win over the Italians. Their two kilometre splits, in comparison with gold and silver ride off, are very promising. I’m pleased with their result.”
The event at the Velodromo Bicentenario in Aguascalientes is the third and final round of the UCI Track Cycling Cup, following Cali and Glasgow.
The meeting continues on Friday with Barker in action in the omnium.