United showed terrific courage though to come back each time and eventually clinch a dramatic win in the dying seconds through David Goodwillie’s winner.
It was the Tannadice outfit’s first win in Govan for six years and it was a result which could prove to be so costly to Walter Smith’s title ambitions.
The fact is though that his team’s task has only got harder and Gers’ destiny remains in their own hands.
If they win their last 10 matches of the campaign, including the post-split meeting with Celtic, they will win their 54th crown by at least a point.
At this stage, however, they are some way from making that happen and the Light Blues must now respond positively on Tuesday at St Johnstone to get on track again.
Manager Smith made two changes to the team which won the League Cup final 2-1 against Celtic on March 20.
Madjid Bougherra remained on the sidelines with the hamstring injury which forced him out of that game while Kyle Lafferty was prevented from playing by a knee problem.
That meant Steven Whittaker moved into the middle of defence as an auxiliary centre half, just as he had done in the derby, with Richard Foster playing at right-back.
El-Hadji Diouf also returned to action from a fortnight of raising his arms aloft to partner Hampden hero Jelavic up front.
The teams emerged to a huge roar after the club’s 114th major trophy had been paraded by two young supporters moments before kick off.
But for all the incentives Gers had to make a strong start and take control of the match early, they were somewhat muted in the opening exchanges.
Jelavic had a chance to head home after some inventive play by Diouf on the left but the Croat was both off target and penalised for a foul in any case.
That aside, it was a fairly even contest to begin with and you would never have known United had come into this one off the back of a 3-0 midweek humbling at Motherwell.
The Arabs knocked the ball around of confidence and looked more like the side which had scored in 24 of their 25 SPL encounters since their last visit to Ibrox in September.
For all that, they were restricted to long-range attempts and both Barry Douglas and Danny Swanson were too high.
With fans desperate to see the hosts move back to the top of the league, it was important for the Light Blues to forge ahead before frustration kicked in.
And after 18 minutes, they earned themselves a most welcome advantage as Jelavic scored his 12th goal of the campaign.
Referee Steve Conroy took an eternity to award a foul a few yards outside the box but when it was eventually given, it presented an opportunity to swing the ball in.
And when Diouf did exactly that with a precise delivery, Jelavic had more room than you would expect to nod in the opener.
Suddenly Rangers had their tails up and the former Rapid Vienna star tried to return the favour but his Senegalese team-mate was blocked as he tried to shoot.
Naismith was also disappointed when his weak claims for a penalty were waved away.
From there, any momentum Smith’s men had frittered away all too quickly and United came back into the game again.
Any time they tried to start something outfield, however, they found Whittaker in inspired form as he snuffed out most things they threw at him.
One of the criticisms levelled at the Scotland international by his detractors is that he sometimes struggles when he’s put under pressure in defence.
But his first-half showing in particular made him look like he had been playing alongside David Weir in the central position for years.
It was unfortunate, therefore, that the one mistake Whittaker made seconds before the break saw him punished as United equalised.
He slid in as Swanson cut across the park but missed and that allowed the midfielder to set up David Robertson.
Despite claims of offside, he held his composure to pick his spot past Allan McGregor and shoot across goal to make it 1-1.
There was to be a good response from Gers though as they moved back in front just six minutes after the restart.
Gregg Wylde forced a corner when Sean Dillon – the scorer of an own goal the last time he was at Ibrox – almost put through his own net again.
When the set piece came in, Maurice Edu nodded down and Naismith’s measured half volley soared over the line.
Within seconds, United were inches from restoring parity as a long ball upfield found Swanson and he held off Wylde.
He then made his way into the box and with everyone expecting a cut back, he beat McGregor at his near post and the shot flashed right along the goal line and wide.
Back came Rangers, with Naismith almost scoring a carbon copy of the goal he had just put his side in front with.
Jelavic too had a chance when Diouf was fouled on the right flank but he blazed well over when he was set up low on the edge of the area.
There weren’t too many major talking points in the second period but as time wore on, the inconsistency of refereeing decisions being made were irking both sides.
One in particular when a throw should clearly have gone Rangers’ way and didn’t drew rage from the home bench.
So much so, in fact, that Smith, Ally McCoist and Kenny McDowall all charged from the bench to remonstrate with linesman Alasdair Ross.
Back on the pitch, Diouf nearly capped a delightful passing move with a cute backheeled finish but away keeper Dusan Pernis was equal to it.
That proved costly 13 minutes from the end when United made it 2-2 with a goal out of nothing.
There seemed to be little danger when Paul Dixon swung a high ball deep into the Rangers penalty area.
But his cross swirled in the air and dropped beyond Weir, with Johnny Russell’s run into the mix timed perfectly and his bullet header flying in.
That made for a nervy end to the contest and it was United who looked more likely to win at first, with McGregor touching a Swanson cross on to the bar soon after.
Indeed, it perhaps took Rangers too long to show the urgency required to win and when Jelavic’s header was saved two minutes from time, it seemed the draw was coming.
But the Light Blues pushed forward looking for all three points – and that’s ultimately what cost them.
With everyone committed to getting a winner, Whittaker hit the bar and United cleared with the home defence posted missing.
That left Goodwillie in the clear with just McGregor to beat and although he could have passed to Craig Conway, he took it on himself and clinched an unlikely success.