After Celtic's humiliation on Saturday, this was an opportunity for the Light Blues to create a gap which would be beyond their Glasgow rivals.
However, in truth Walter Smith's side were fortunate to leave Tannadice with a point.
In an opening first half dominated by the hosts, Rangers' first glimpse of goal came courtesy of a Lee Wilkie error giving the ball to Nacho Novo, who blasted over from the edge of the box.
After wasting a number of opportunities, the Terrors were eventually rewarded for their efforts in the 37th minute.
Kris Boyd clattered the heels of Willo Flood who stood up and curled in a free-kick which Darren Dods headed down.
Allan McGregor brilliantly saved and Christian Kalvenes cracked the follow-up off the post, but forced his second attempt over the line.
But the lead lasted only four minutes when a needless foul by Dods on Boyd saw Barry Ferguson curl in a free-kick for David Weir to bullet in a header from six yards.
United restored their lead in the 51st minute with a header from Noel Hunt.
A Kalvenes deep cross from the left was chipped back by Sean Dillon and, while his lob appeared to be going in, the little striker made sure by knocking in from virtually the goalline.
Rangers almost equalised in the 57th minute with a thunderous Ferguson volley which flew across the goal.
However, the champions-elect were level one minute later when Lee McCulloch sent Novo racing in on goal and he rounded the keeper to net.
But in this pulsating match, United stormed ahead for the third time with an own goal from Carlos Cuellar in the 65th minute.
A curling cross from Dillon appeared to be heading for David Robertson, but the Spaniard volleyed into the roof of his own net.
United pressed to close the game but instead they gifted an equaliser two minutes later in a disastrous repetition of last month's CIS Insurance Cup final meeting of the same two sides.
This time it was Flood who gave a short pass back for Boyd to gratefully accept and hit the ball in off the post.
In a thrilling climax, the Terrors could and should have grabbed a couple of goals, while Rangers could have scored one but in the end both teams settled for a share of the spoils.