Sophia Smith drew out the Welsh goalkeeper and crossed to Rodman, who finished into an open goal to break the deadlock in the 76th minute in San Jose, California.
Rodman, who came on as a second-half substitute after coach Vlatko Andonovski opted to start Alyssa Thompson up front, added another goal 11 minutes later.
"They were organized, they were disciplined. They defended well and it made it hard for us," Andonovski told reporters after the match.
"(Trinity) was one of the players ... that had a task to fulfill to raise the pace and the tempo of the game a little bit. And we saw that the tempo changed dramatically."
The US had not been held goalless in the first half since January but were utterly flummoxed against the 30th-ranked Wales' tight formation, before Andonovski sent on a flurry of substitutes, including Rodman.
"Today was another stepping stone for us," veteran defender Crystal Dunn said in a post-match interview. "Obviously wasn't our tidiest game, but I think this is a great moment for us to build on what we're working on right now."
The friendly gave fans a final glimpse at their four-times champions before they travel to New Zealand, where they begin their World Cup campaign against Vietnam in Group E on July 22.
The 23-player squad are in pursuit of an unprecedented third consecutive title and were treated to a post-match ceremony in front of 18,000 fans before they were expected to board a plane hours later.
Veteran Megan Rapinoe, who announced on Saturday that she would retire at the end of the season, did not play in the match but was greeted to roars of celebration as she stepped out onto the pitch and gave the crowd a wave.
Rapinoe is travelling to her fourth World Cup despite suffering a minor calf injury playing for her OL Reign club last month. Andonovski said he had no concerns with her recovery timeline.
"We didn't want to rush anything. There was no need for it," he said. "We knew that we have the quality that we need to overcome the challenges that were ahead of us and wanted to give Megan just a few extra days."
The World Cup kicks off on July 20 in Australia and New Zealand.