The Tannadice lads gave an outstanding performance to convincingly defeat a much more experienced St Mirren side at Airdrie.
The breakthrough came after 18 minutes when, after good work by Jordan Allan, Brad Smith cut the ball back to Jamie Montgomery who drilled home from the edge of the box.
Saints enjoyed plenty of possession but only tested United keeper Marc McCallum once when he brilliantly beat away Lewis McLear's first time effort.
United almost doubled their lead immediately after the restart, Montgomery firing inches over after being put through by Aidan Connolly.
Another fine save when palming away an Adam Campbell effort kept the Tangerines' lead intact five minutes later.
But United did increase their lead after 59 minutes with Allan again the architect. He played the ball inside to Aidan Connolly who slipped into the path of Scott Smith who netted from an acute angle.
Saints threatened to get back into the game with Campbell again denied by McCallum, while a terrific last gasp block by Euan Spark kept out a Thomas Reilly effort.
However, with six minutes left, the home side scored a brilliantly worked third when the ball was played out to Montgomery and from his cross substitute Regan Tumilty sent a diving header just inside the far post.
Dundee United: McCallum, Spark, McLaughlin, S Smith, Harwood, H Souttar, B Smith, Montgomery, Allan (Tumilty 81), Fraser, Connolly. Subs not used: McGovern, Russell, Carrick, Malcolm.