Aberdeen almost went ahead in the first minute, Alan O'Sullivan drilling in a shot from an acute angle, but Joe McGovern pulled off a terrific stop.
In response, Scott Smith fired narrowly wide from 20 yards shortly afterwards.
And he enjoyed better luck with 14 minutes gone, firing in a shot from 12 yards which went in off a Dons defender in his despairing attempt to keep it out.
Although the outstanding Scott Smith twice went close before the break, the visitors came close to levelling when Michael Rose's crashing effort flew inches wide.
And the Dons went even closer to levelling early in the second half, McGovern blocking a powerful McManus effort with his legs.
Late on, Scott Smith capped his superb performance with a goal-line clearance.
Dundee United: McGovern, Montgomery, McLaughlin, S Smith, Butcher (Allan 52), H Souttar, B Smith, Malaga, Tumilty (M Smith 84), Fraser, Connolly.
Substitutes not used: Anderson, Russell, Robson.