Goals from Nikica Jelavic and Kyle Lafferty sealed the points, with the Scottish champions now hoping to wrap up the championship in the last match of the season against Kilmarnock at Rugby Park on Sunday.
Of course, Rangers could be celebrating before then if Celtic lose at Hearts on Wednesday night and gift the trophy to their bitter rivals.
Fans paid their own tribute to the outgoing manager in the form of a banner which stated his achievements over two spells at Rangers: 'League champions nine times, Scottish Cup winners five times, League Cup winners six times, thank you Walter Smith.'
The Ibrox faithful will now be hoping the number of titles will stand at 10 by the time Smith bows out this weekend.
Rangers named the same side who had notched up 4-0 and 5-0 wins over Hearts and Motherwell respectively in their last two games.
United - who suffered a 4-0 defeat at Tannadice the last time the two teams met - opted for a defensive approach and Jon Daly was dropped despite scoring a hat-trick at the weekend, as David Robertson was drafted into the side.
New Rangers owner Craig Whyte was again in the stand and was spotted deep in conversation before the game with Donald Muir, who was previously Lloyds Banking Group's representative on the board before his resignation as a non-executive director on Friday.
On the pitch, Rangers could have been ahead when a Steven Davis corner broke for Steven Whittaker and his long, low shot was blocked before Jelavic saw his rebound strike smothered by goalkeeper Dusan Pernis.
Jelavic then had another effort saved at the near post by Pernis, with Lafferty loitering with intent in front of an open goal, before the Croatian sent a header flashing just wide of the upright.
Rangers continued to pile on the pressure and only the woodwork prevented them from grabbing the opener when Lafferty's ferocious shot crashed off the post.
The home side's hard work paid off when they netted two quick-fire goals in the space of four minutes.
Jelavic set the ball rolling after 21 minutes when he met Whittaker's cross and bulleted a header past the grasp of the United goalkeeper from 10 yards.
Lafferty then raced on to a lovely through ball from Steven Naismith before stroking a right-foot shot into the back of the net to double the advantage.
Rangers started the second half strongly and could have extended their lead had Sasa Papac been able to connect cleanly in front of goal with a Jelavic ball into the danger area.
The striker turned provider again moments later, this time whipping across the face of goal for Lafferty, who just failed to connect at the back post and stab home his second of the night.
Rangers threw Lee McCulloch - who made his comeback from knee surgery at the weekend - into the action for youngster Gregg Wylde with 65 minutes gone.
United could have hauled themselves back into the game when Craig Conway's corner found Scott Robertson and his bullet header was held by goalkeeper Allan McGregor at his near post, before Robertson made way for the introduction of Prince Buaben.
Any hopes of a United comeback could have been snuffed out when Maurice Edu won a free-kick just outside the area and Jelavic's swerving effort fell just off-target.
McGregor was called into action again as the game entered the final 10 minutes, when he produced an impressive save to deny substitute Daly.
But, on a night which also saw skipper David Weir celebrate his 41st birthday, Rangers held on to pile the pressure on Celtic in a nerve-shredding climax to the campaign.