Paul McMullen got them underway when he finished a Billy King cross, and shortly after it was 2-0 when King scored with a long-range shot.
Mark Durnan volleyed in a third to give the visitors a commanding half-time lead against the Highland League side.
The result was marred with United striker James Keatings carried off.
The result at Victoria Park gives Ray McKinnon's men six points out of six following the 2-0 win on Saturday over Raith Rovers.
Three first-half goals moved Dundee United three points clear at the top of Scottish League Cup Group C as they eased past Buckie Thistle.