Falcao's 33rd goal for his country came after a penalty was awarded for a handball by Japan's Takehiro Tomiyasu in the 64th minute in Yokohama.
Colombia's triumph was a small measure of revenge for the defeat they suffered by Japan in the group stage of last year's FIFA World Cup and gives former Iran boss Queiroz the perfect start to his tenure.
After Sebastian Villa struck the crossbar in the fourth minute for the visitors, it was Japan who were the better team in the first half, having a host of shots without really testing Colombia goalkeeper Camilo Vargas.
However, Colombia looked more comfortable with Queiroz's system after half-time and had two goals disallowed, the first for handball and the second for offside, either side of Falcao's winner.
Falcao celebrated his goal by raising a shirt bearing the name of team mate Juan Fernando Quintero, who injured his anterior cruciate ligament playing for River Plate last weekend.
Tomiyasu had a great chance to make amends for his handball 13 minutes from the end but headed straight at Vargas.
The ever-lively Shoya Nakajima, one of the players to shine for Hajime Moriyasu's side, also went close, clipping the crossbar with a long-range effort.
Colombia substitute Luis Diaz also hit the bar in stoppage-time but it didn't matter as they secured victory to continue their preparations for the Copa America in Brazil in June.
They next play Korea Republic on Tuesday, while Japan, as one of the two invited nations for the Copa, will have another chance to test themselves against South American opposition when they take on Bolivia.
They are without captain Maya Yoshida and striker Yuya Osako, who are being rested as some European clubs have raised concerns about the amount of football their Japanese players have been participating in.
The loss to Colombia was their 13th match since going out to Belgium in the last 16 of the 2018 FIFA World Cup in Russia.
