Swanson missed last year's women's World Cup with a knee injury and she quickly dispelled the team's goalscoring concerns by grabbing the double in a dream first half for the USA on Thursday after Trinity Rodman's opener in Nice.
After the US went 2-0 up, they immediately won the ball back in Zambia's half before Swanson scored her second to break former skipper Lloyd's record from the 2015 World Cup final.
"Not an easy journey for her but she has been resilient and persevered through it all. Still has a lot more in her ceiling. Proud of her!" the former skipper said on X.
Coach Emma Hayes, who took over the US role in May, also earned her first competitive win.
"The first part of the first half was exceptional. To come out the way we did, the intention, the intensity, the decision-making, the execution should have been at least five (goals) at halftime," Hayes said.
The US are looking to rebound from their failure at the World Cup where they were knocked out in the last-16 -- their worst finish in the tournament's history.
They will aim to carry their momentum into a tougher test in Marseille on Sunday against 2016 gold medallists Germany, who kicked off their campaign with a resounding 3-0 win over Australia.
"There were things within our structures I didn't like in the first half, but that's easy fixes," Hayes added.
