The home side had the best of the early chances when John Fleck tried an opportunist shot from distance, John Gibson, the visiting 'keeper, parried the strike to Stephen Stirling but the ball just wouldn't lie properly for the midfielder to get in a clean shot and eventually the danger was cleared .
In the 19th minute a run down the right and into the box from Andy Shinnie saw the 'Gers skippers cross blocked. From the resultant Fleck corner kick Andy Little rose but failed to meet the ball cleanly and his effort struck the bar.
As the match ebbed and flowed Scott Gallacher was solid as a rock in the home goal and confidently caught every incoming cross, however the 'Gers stopper pulled off a great point blank save when Johnny Russell fired in a goalbound shot.
The Champions responded with attempts from Stirling and Efrem, the Cypriots attempt brilliantly saved by Gibson when faced one on one.
Gallacher was again called on to deny Russell when the Tannadice striker let fly on the volley just before the break.
Half Time - Rangers 0 Dundee United 0
United almost broke the deadlock 9 minutes after the interval when Gallacher was forced to clear with his head outside the box only for the ball to fall to the visitors, however when it was played into Jordan Love with the open goal gaping the young striker took his eye off the ball and missed it completely.
Love was the villain again for the Tayside team when his header flew across the face of Gallachers' goalmouth from a corner when it looked easier to score.
The match was soon to turn in favour of the home side and the Tangarines were about to rue their missed chances as Rangers started to gain the upper hand.
Efrem set up Jamie Ness but the midfielders attempt went inches over. Then it was the turn of Scotland Internationalist Andy Shinnie to threaten, firstly missing a golden chance from 2 yards out and then again moments later from yet another corner.
However it was to be only a matter of time before Shinnie finally hit the back of the net and he did so with only 15 minutes of the match remaining.
Picking up the ball on the edge of the 18 yard box he moved inside his marker before unleashing an unstoppable shop past Gibsons near side.
The breakthrough signalled the end for Uniteds' challenge and Gibson was forced to pull off a fingertip save from Efrem as the Murray Park side homed in on the three points.
With 85 minutes on the clock referee John McCrossan adjudged Phil McGrath to have shoved Kyle Hutton in the box and awarded the home side a penalty kick, one which was put away with aplomb by John Fleck.
With the points now safe and only 2 minutes left Willie McLachlan played a perfect pass down the right flank to Craig McShea who darted for the bye line before cutting a pass back across goal to Kyle Hutton who twisted and placed his shot passed the outstretched arms of Gibson and into the corner of the net for 'Gers third. To their credit United still showed fighting spirit and their most outstanding player, Johnny Russell, could consider himself unfortunate when his volleyed shot crashed off the crossbar with almost the last kick of the match.
The result now just leaves Rangers requiring one point from Friday's match at home to Motherwell to retain the coveted Title for a second successive year.
The Teams;
Rangers - Gallacher, McLachlan, Kinniburgh, Little, Harvey, Ness, Stirling (Hutton 65), Shinnie, Bagci (McShea 73), Fleck, Efrem
Subs not used - Vaiculis, Craig, Durie, Forbes, Campbell.
Booked - Harvey 65 & McLachlan 68
Dundee United - Gibson, Billy Russell, Fleming, McGrath, Pope (Smith 62), Ryan McCord, Scott (Mathieson 69), Ross McCord, Love (Boyle 78), Johnny Russell, Paterson
Subs not used - Cannon, Dow, Anderson, Stokes
Booked - McGrath 85
Referee - John McCrossan
Assistants - Gerry Durning & David Munro
Attendance - 141