The fourth seed stamped his authority on the encounter from the outset, and assumed complete control of the opening set with two comprehensive breaks of serve.
Murray took the set 6-2 with consummate ease, with the British number one finding a good rhythm on serve and from the back of the court.
Falla clawed his way back into the match in a hard-fought second set, but the Colombian could not prevent Murray eventually taking control once more.
The Scot slammed a flurry of fine groundstrokes to break once more, and the world number four took the second set 6-3 to make it look easier than it was.
"I was expecting it to be tricky ... and managed to play better," said Murray.
"Once I settled down and started playing well, I was in most of his service games. So I was putting pressure on him."
The fourth seed faces a third-round clash with 26th seed