The U.S. were too strong physically for the lightweight South Americans, who were never allowed to settle into their close passing game, and they could easily have doubled their tally as they dominated the Group C game in Sinsheim.
Heather O'Reilly opened the scoring with a powerful, dipping 25-meter shot in the 12th minute before Megan Rapinoe and Carli Lloyd scored in a seven-minute spell early in the second half to finish off the match as a contest.
"Sometimes we were really good, sometimes not so good," said U.S. coach Pia Sundhage, who faces her native Sweden in the final group game.
"We need to work on controlling the game regardless of whether it's defense or attack, sometimes we are too eager to find the final pass instead of keeping it."
The U.S., who have not conceded a goal so far, had already missed several chances before O'Reilly fired them in front against opponents who are taking part in the finals for the first time after qualifying at the expense of Argentina.
Shortly afterwards, Colombia lost possession and Rodriguez found herself free again only to shoot wide.
However, the U.S. made the breakthrough when Colombia's Liana Salazar failed to control the ball which fell to O'Reilly whose powerful effort left Sepulveda helpless.
They could have paid dearly when Katerin Castro had the ball in the net for Colombia in first-half stoppage time but her effort was disallowed for offside.
That appeared to rattle the U.S. who quickly finished off the game after the break.
Rapinoe made it 2-0 five minutes into the second half with an emphatic finish after being set by Lauren Cheney's incisive pass.
Lloyd added another with a long-range shot that slipped through Sepulveda's hands seven minutes later.
Rapinoe and Wambach then both hit the woodwork against the flagging Colombians in the closing stages.
(Writing by Brian Homewood in Berne; Editing by Ken Ferris; To comment on this story: firstname.lastname@example.org)