Nikica Jelavic and Kyle Lafferty struck in quick succession in a first half where the champions in waiting battered their opponents in a pulsating opening 30 minutes.
They could now win the title as soon as tomorrow if Celtic lose to third-placed Hearts at Tynecastle.
If that doesn’t happen, a win at Kilmarnock on Sunday will be enough to secure a world record 54th championship.
On this form, you wouldn’t expect anything else from a Gers team which is clearly saving its best for last this term.
This triumph was their eighth in their last nine games and they have now recorded a fantastic 15 clean sheets in their last 20 league outings.
Smith was modest in the build up to this fixture, his very last at home in his two spells at the Light Blues helm before he leaves his post in the summer.
But he will have been so pleased at the way his players ensured he signed off with a win which leaves him with one hand on his 21st major honour.
This was an emotional victory and it is hard to believe his players won’t now deliver for him in Ayrshire, should they have to wait that long.
For the fourth match in succession, Smith named the same starting XI and he went with the seven men who began on the bench against Hearts as his replacements.
The teams emerged from the tunnel to a cacophony of noise but once play got underway, you could sense nerves in the air initially.
Gregg Wylde’s hesitancy allowing Keith Watson to get a shot away, albeit over the crossbar, did little to ease them.
But the Light Blues soon found their rhythm and a wonderful passing move between Steven Naismith, Jelavic and Lafferty very nearly paid off.
Steven Whittaker went close moments later with a wicked volley and when it was blocked, the rebound fell to Lafferty who was on target but saw his shot saved.
The Light Blues were playing some lovely one-touch football and Jelavic, Naismith and Whittaker almost combined to create a magnificent team goal.
Lafferty then agonisingly saw his curled attempt crash off the face of the post as Gers did everything but score in the opening 15 minutes.
There was a clear determination to get in front early and Jelavic was next to have a go from a similar position to the one he scored against the Jambos from on Saturday.
This time, however, his shot was wild and wayward as it twisted and turned beyond keeper Dusan Pernis’ far post.
Jelavic was not to be denied though and he continued his impressive scoring run with the opener after 21 minutes.
Whittaker took a short throw to Naismith and received the ball back again before swinging in a left-footed cross towards the near post.
Up rose the £4million man and with a touch off the back of his head then his shoulder, his effort looped beyond Pernis and in.
One soon became two as Rangers doubled their advantage four minutes later with another fine strike.
It is quickly becoming the case that when Jelavic scores, Lafferty does too and sure enough the big Ulsterman found the net again to make it 2-0.
Naismith was the provider with a surging run through the heart of midfield and when he released the ball, he found the Northern Ireland star.
He did the rest as he passed in his 12th club goal of the season and fourth in five matches so coolly to ensure this will be his best scoring campaign with the club yet.
It was perhaps to be expected after such a frenetic start that Gers’ tempo would drop and, sure enough, the Arabs started to enjoy a little more possession.
But they couldn’t make it count and the hosts went into the half-time interval with their strong advantage intact.
It had been a strange decision by visiting manager Peter Houston to bench Jon Daly after he had scored a hat-trick against Motherwell last time out.
By the same token, it was no surprise to see him called into action for the quiet Johnny Russell at the restart as United sought a way back into the game.
It was Rangers who were to press on again though and a flowing move involving Whittaker, Naismith then Jelavic nearly ended with Lafferty grabbing his second.
As it was, he couldn’t quite connect with the Croatian’s measured cross and he slid into the net without the ball.
Jelavic should have done better when Davis threaded him in and he chose to chip Pernis, something the keeper was in tune with as he gathered comfortably.
Although the Light Blues were having the better chances, United still came forward with purpose and that made the home support restless.
Lafferty tried to ease the jitters with a crisply-hit attempt at the back post but Pernis did well to smother at the post.
At the other end, it took a good covering header from Davis to bail out Allan McGregor before the keeper caught well from Scott Robertson.
Although less than 20 minutes remained, Rangers were needing a third goal to make the points safe.
And when Maurice Edu was fouled 30 yards out, Jelavic had a chance to seal the game with a free kick but bent a good shot just over.
He went close again with a firm header from a Davis corner after good work by Whittaker but Pernis just kept him out.
To their credit, United had been outplayed for large spells yet they continued to make a game of it.
Substitute had hearts in mouths as he cracked a fierce drive off McGregor’s right-hand post with the keeper well beaten.
The same applied when Madjid Bougherra and the otherwise sound David Weir made a meal of clearing in front of their own goal.
Whittaker provided a touch of respite with a shot which Pernis had to scramble away before substitute Lee McCulloch blazed over.
But by now, with less than three minutes plus injury time to go, the support was growing in confidence again as they could see victory in their sights.
As the seconds ticked down, the volume cranked up and when Calum Murray’s final whistle went, it left Rangers in a superb position.
Now all eyes turn to Tynecastle with the reigning champions looking ever more likely to keep their crown.