Spurs dominated the Premier League champions for lengthy spells but went into the break trailing 1-0 thanks to Wayne Rooney's header.
Emmanuel Adebayor had earlier tested United keeper David De Gea and seen a goal disallowed for handball.
But Harry Redknapp's men fell further behind on the hour mark when Luka Modric switched off and allowed Nani to weave his way to the byline before cutting the ball across.Tottenham appeared to have cleared the danger courtesy of a goalline clearance, only for Young to swivel and volley home past Brad Friedel.
The England man, who had provided Rooney's goal with a sweetly-struck corner, saved his best for last.
United skipper Patrice Evra rolled the ball into his path and Young drove forward before leaving Friedel well beaten with an exquisite curling effort.
The hosts continued to look for a way back into the game and substitute Jermain Defoe cut the arrears three minutes from time with a dipping drive.
But it proved to be too little, too late as United comfortably held on to move back within two points of league leaders Manchester City.
