Jairo Arrieta also scored as the visitors cruised to a comfortable win in a clash of clubs with revamped rosters.
Federico Higuain bagged a brace for Columbus after Jairo Arrieta opened the scoring, giving Crew coach Gregg Berhalter his first MLS win.
New United left back Cristian Fernandez provided the game's first chance on goal, firing a 40-yard effort that forced goalkeeper Steve Clark to tip the shot over the crossbar.
But it was the visiting Crew who broke through in the 18th minute, with right back Josh Williams connecting with a Hector Jimenez flick and whipping in a low cross that Arrieta slotted home.
The Crew doubled their advantage nine minutes later when United midfielder Perry Kitchen was ruled to have taken down Michael Parkhurst in the box, setting the stage for Higuain to emphatically slam his penalty kick into the upper corner.
United nearly halved the deficit five minutes after halftime when a Nick DeLeon cross was tipped into the air by Clark and headed off the line by Parkhurst.
Columbus finished the scoring in the game's dying moments as Higuain converted a low service from substitute Justin Meram.