A win or tie for the United States would have been a boost for a team which failed to qualify for the World Cup in Russia after losing to Trinidad and Tobago a year and a day ago.
But it was not to be.
Colombia thoroughly outplayed the U.S. in the first half on a hot and humid night in Florida, and drew first blood in the 36th minute when Rodriguez curled a left-footed shot into the top left corner.
With Christian Pulisic, Weston McKennie and Tyler Adams all unavailable due to injuries, interim U.S. head coach Dave Sarachan made no changes at halftime but his team came out more energised after the break.
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Kellyn Acosta latched onto a long pass in the box from Antonee Robinson to level the game in the 50th minute.
The U.S. took a 2-1 lead three minutes later when Timothy Weah found space on the left wing and delivered to Bobby Wood, who split two defenders to score.
Colombia's Carlos Bacca squared the contest three minutes later, however, with a shot past the diving arms of keeper Zack Steffen.
Colombia nosed ahead in the 74rd minute, with Radamel Falcao capitalising on a defensive breakdown to score, sending the team's yellow-clad fans into a frenzy.
Colombia put the game away in emphatic style in the 79th minute when Rodriguez found Miguel Borja across the box and the forward hammered a volley into the corner.
Next up for the U.S. is a friendly against Peru on Tuesday in Connecticut. Colombia battle Costa Rica on the same day in New Jersey.
(Reporting by Rory Carroll; Editing by Ian Ransom)
