Falcao headed home on 56 minutes to cancel out Willian’s superb opener for Brazil in a result which boosts Colombia’s hopes of qualification for next year’s finals in Russia.
Brazil have already qualified for the World Cup and are guaranteed first place in South America’s standings. The draw saw second-placed Colombia move to 26 points from 16 games.
Colombia had started brightly, with James Rodriguez testing Brazilian goalkeeper Alisson with a low shot after a deftly worked one-two on 23 minutes.
Brazil had another scare in the 33rd minute when Thiago Silva saw a headed clearance loop towards his own goal forcing Alisson to tip over the bar.
Alisson meanwhile was alert shortly before half-time, comfortably dealing with a Rodriguez free-kick after Paulinho’s foul on Juan Cuadrado.
On the stroke of half-time however Brazil conjured a goal out of nothing.
A long ball forward found Neymar just inside the area and the Paris Saint-Germain star produced a sublime touch to roll the ball invitingly into the path of Willian.
The Chelsea midfielder glanced up and uncorked a stunning half-volley with the outside of his right boot which flew into the top corner.
Colombia however did not have long to wait to get back on level terms with a goal through Falcao on 56 minutes.
Santiago Aras did well down the right flank and picked out the AS Monaco striker with a pinpoint cross which the Colombian talisman stooped to head home.
Rodriguez might have given Colombia the lead soon afterwards but his curling free-kick hit the woodwork after beating Alisson.