However, second half goals from Keith Watson, Stuart Armstrong, Ryan Gauld and David Goodwillie saw the visitors finally overcome 10-man Kilmarnock.
A late consolation goal from Kris Boyd allowed the former Rangers striker to claim his 175th top flight goal and overtake Henrik Larsson's haul.
With wind and rain lashing the length of the Rugby Park pitch, both sets of players had difficulty dealing with the elements.
Although the conditions better suited the tight passing United style of play, Kilmarnock stuck manfully to the task of containing the high flying Tannadice side, even after Gabriel Reuben was sent off after only 22 minutes.
The first half saw a handful of yellow cards directed towards Killie players, with Manuel Pascali - just back from suspension - earning the first after 11 minutes for bring down Gauld.
The first goalmouth action cam after 14 minutes when Rory McKenzie's cross bounced high inside the box allowing Jackson Irvine to produce an overhead kick, which forced a comfortable save from Radoslaw Cierzniak.
Three minutes later Reuben was rather harshly booked when Stuart Armstrong tumbled over the Killie midfielder. Soon after Armstrong clattered into Reuben, without punishment.
However when the same two players clashed in the middle of the park, Reuben's trip on the United man earned him his second yellow inside five minutes and reduced the home side to 10 men with three quarters of the game remaining.
United tried to utilise their extra man and Andy Robertson's cross picked out Brian Graham - but his half-hit shot was easily gathered by Craig Samson.
Then after 29 minutes Graham came within inches of the opening goal when his downward header, from a Gary McKay-Stevens cross, bounced narrowly past the post.
Samson produced the first real save of the game in the 34th minute, when at full stretch low to his right he brilliantly palmed a curing free-kick from Gauld round the post.
The referee was the busiest person on the park though and by half-time he had added the names of Irvine and Sean Clohessy to his list of bookings, leaving the hosts under more pressure in the second half.
A man down but with the wind at their backs Kilmarnock made a positive start to the second half. A turn and shot from Boyd tested the goalkeeper before Jackson sent a header over the crossbar.
A quick break from United and through-ball from Gauld sent Mackay-Steven to the line but his cutback for Graham was well cut out by Samson.
The Killie keeper was helpless, though, after 59 minutes when United opened the scoring.
Play moved down the hand side of the box and when Armstrong laid the ball across the front of goal, Keith Watson rattled it high the net from four yards to put United ahead.
A minute later the home side had strong appeals for a penalty denied after Chris Johnston's shot from the edge of the box cannoned off John Soutar's arm.
Intent on grabbing a second to wrap up the points, United replaced Graham with leading scorer Nadir Ciftci, after 72 minutes.
However, Armstrong grabbed the second goal two minutes later. Again he attacked the Killie box on the left but continued his run before nudging the ball past Samson.
It really was game over within a minute when Armstrong robbed Ashcroft before forcing a great save from Samson. However, the ball fell kindly for Gauld, who rolled it into the empty net to make it 3-0.
Three minutes from time Boyd netted his historic goal when he headed Rory McKenzie's cross high into the net.
But United claimed had the final say with a fourth goal in the final minute when substitute David Goodwillie rifled the ball home after Andy Robertson clattered into Samson.