Steve Campbell's Under-19 side were unfortunate to be knocked out of the SFA Youth Cup at the Semi-Final stage after a tense and entertaining encounter at Tannadice.
Having had two strong penalty claims denied in the first half, United found themselves 1-0 down at the break through a John Fleck goal. Defender Gordon Pope equalised ten minutes into the second half to take the game into extra time, but Rangers' lead was restored four minutes into the first period by substitute Andrew Little.
The home side rallied and Jonny Russell struck the crossbar with a terrific effort in the second period of extra time, but with United pushing forward in injury time another substitute - Chris Craig - added a third.
United opened the game brightly, a long range Russell effort parried over the bar by Rangers goalkeeper Gallacher on six minutes. Five minutes later, Ross McCord's free kick was deflected wide, while Ryan Dow combined well with Russell shortly after that.
After collecting a return pass, Dow beat one defender on his way into the area, but was denied a shooting opportunity by the timely challenge of Perry.
Within a minute, though, Rangers went in front against the early run of play. Isa Bagci got between two United defenders, and with Gibson advancing, the Turkish striker squared for John Fleck to clip a shot into the net from twenty yards.
The goal gave more confidence to the visitors going forward, and Gibson saved well from a long range Efrem effort midway through the half.
United responded though, and just before the half hour, they had a strong shout for a penalty when Russell appeared to be brought down in the area, but the referee waved play on, with the striker cautioned for his protestations.
Sean Anderson had a shot well saved, before the action swung back to the other end. Gibson blocked well as Fleck caught United on the counter, while Bagci directed a header straight at the United 'keeper from Efrem's cross.
Rangers centre half Ross Harvey blazed over the bar from a good position a minute before the break, before United's second penalty claim was turned down.
Ross McCord retrieved the ball on the bye-line, and turned his defender on the left side of the penalty area. There appeared to be a clear trip, with all eyes turning to referee Stevenson to see if he determined the offence to be inside or outside the penalty area. To the bewilderment of virtually everyone, however, the official waved play on.
Half Time: Dundee United 0-1 Rangers
United's youngsters again started brightly in the second half. Gordon Pope's cross from the left was stabbed goalward by Dow, but Perry blocked at the expense of a corner.
The resulting corner was half cleared, but the ball was played back into the danger area and in the ensuing scramble, the ball broke back for Gordon Pope to lash into the net from ten yards.
Three minutes later a great run from Anderson took him into the area, but his shot lacked conviction and allowed Gallacher to save. Russell then got himself in front of Harvey to meet a cross from the left, but his effort was again too close to the Rangers goalkeeper.
With United aggrieved at two penalty claims in front of The Shed having been turned down in the first half, it was Rangers turn in the second half, when Efrem went down but instead of seeing the referee award a penalty to his side, he received a caution for simulation.
As legs began to get tired late in the game, there were chances for either side in the closing minutes. A deep cross from the left was plucked out the air by Russell who laid off for Anderson, whose shot was blocked, before Gibson saved from Little and Shinnie headed over.
After 90 minutes: Dundee United 1-1 Rangers
Four minutes into extra time, United substitute Scott Paterson checked back and shot for goal, but Gallacher saved.
Just as in the first half however, Rangers broke up to the other end and struck on the counter. Andrew Little latched onto a ball played into the left side of the penalty area, and his powerful shot beat Gibson and found the bottom corner.
Ross McCord's free kick on 104 minutes curled just over the bar, but showed that United hadn't given up hope.
After the break in extra time, United again looked for a second equaliser. With ten minutes remaining, Jonny Russell picked up the ball 25 yards out, took a touch and shaped himself for a curling effort from twenty yards.
Left-footed, Russell set the ball off well outside the line of the far post, and watched it curl and dip well beyond the reach of Gallacher, but cruelly crash back off the bar.
Much as United pushed and tried to get forward for an equaliser, fatigue was setting in and deep into injury time, Rangers scored a third when the lively Efrem got into the area and cut back for Craig to score.
Full Time: Dundee United 1-3 Rangers (after extra time)
Teams:
Dundee United:
Gibson, Milligan, Fleming, McGrath, Pope (Smith 99), Ryan McCord, Ross McCord, Anderson, J.Russell, Allan (Paterson 63), Dow (Boyle 81).
Subs not used: Cannon (gk), B.Russell.
Booked: J.Russell (29), Paterson (113)
Rangers:
Gallacher, McLachlan, Kinniburgh (Durie 120), Perry, Harvey, Stirling, Ness (Craig 68), Shinnie, Bagci (Little 68), Fleck, Efrem.
Subs not used: Vaiculis (gk), Hutton.
Booked: Efrem (73), Shinnie (102)
Referee: Stuart Stevenson