Falcao converted a second-half penalty in Colombia's 3-1 victory over Kuwait to take his international tally to 24 goals in 56 appearances, the same amount as former striker Arnoldo Iguaran.
Monday's result in Abu Dhabi capped a successful international period for Falcao, who scored three goals in two matches, having only managed four in 22 appearances at Old Trafford this season.
"I am happy to have scored but the most important thing is the victory for the team," the 29-year-old said afterwards.
"Today, we played a good team in the shape of Kuwait who created several chances and that helps us prepare for similar situations in future matches.
"These wins will help to build confidence for the Copa America [hosted by Chile and gets underway on June 11 with Colombia drawn alongside Brazil - who edged them in the World Cup quarter-finals last year - Peru and Venezuela]."
Falcao - on loan from Monaco - returns to Manchester with fourth-placed United preparing to host lowly Aston Villa in Premier League action on Saturday.
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