The result in the first leg makes the Glasgow giants clear favourites to progress to a semi-final tie with Hibernian, but the Doonhammers will be aware that they can perform without pressure as they target a first season among Scotland's elite.
Ever since their demotion to the Scottish Third Division, Rangers have been working towards the opportunity to regain their place in the top flight of Scottish football and Sunday's second leg represents an opening to keep their dream alive for this season.
Both on and off the pitch it has been a turbulent time for the Glasgow giants, but Stuart McCall has ensured that they can still end an indifferent season on a high.
Since his appointment, the former Gers midfielder has guided the club to six wins and five draws in 12 games, a vast improvement on the doomed reign of Kenny McDowall.
Three of the club's last six games have ended in draws, but McCall will be delighted with their response since suffering a comprehensive 3-0 defeat to Queen of the South at the start of April.
That loss threatened to derail McCall's earlier work, but his Rangers outfit are showing character in grinding out results and a decisive touch in the final third, with 14 goals being registered in their last six fixtures.
All of that will count for nothing if they can't avoid defeat on Sunday, but with McCall motivated to take the team back to the big time and the club desperate to renew their rivalry with Celtic, they are well placed to take advantage of their slender lead in the tie.
Recent form: WDWDDW
Queen of the South
After getting the better of Rangers during the regular season, Queen of the South would have fancied their chances of inflicting further misery on their opponents when they discovered that they would meet them for a fifth and sixth time since August.
However, the 2-1 setback last weekend was a hammer blow to their ambitions of a surprise appearance in the top flight, and although they will still back themselves to win on Sunday, James Fowler and his side will be aware that they face an uphill struggle to break Rangers' hearts.
Queens under-performed during the final three games of the season, but Fowler would have been impressed with their display in the first leg, despite their defeat.
They matched their opponents in every department and it was only a stunning free kick from Steven Smith that changed the course of the match. They had chances to establish a lead of their own in the closing stages, but they eventually succumbed to a well-worked goal from the visitors.
One positive that came from Saturday's game was the goal from Derek Lyle, who netted his 20th strike of the season. That effort was his first in three games and his involvement in attack will be key as his team chase the game in front of what is expected to be a capacity crowd at Ibrox.
Queen of the South managed to avoid defeat on their last visit to Glasgow, but they will need to break new ground if they are to progress through to the semi-finals.
Recent form: WWDWLL
Rangers skipper Lee McCulloch has been rated as 50-50 to return to the squad after missing the first leg through injury.
McCall has also revealed that defender Bilel Mohsni is in contention after taking part in training this week.
Barring any late fitness issues, Fowler should have the same squad at his disposal, but changes could be made for the trip to Glasgow.
Rangers possible starting lineup:
Bell, Foster, Zaliukas, McGregor, Wallace, Shiels, Law, Murdoch, Smith, Miller, Vuckic
Queen of the South possible starting lineup:
Clark, Dowie, Durnan, Higgins, Holt, Kidd, McKenna, McShane, Carmichael, Reilly, Lyle
Head To Head
Rangers and Queen of the South have met on nine occasions in competitive fixtures, with Rangers prevailing on five occasions and Queen of the South just twice.
However, after Rangers dominated their first five meetings, Queens responded with an unbeaten spell over a three-game period.
Their most recent win came on April 9 at Palmerston Park when they ran out convincing 3-0 victors, but after their win in the first leg, it will be Rangers who hold the momentum heading into the second leg.
We say: Rangers 2-0 Queen of the South
Playing without pressure should suit Queen of the South, and Rangers have slipped up at Ibrox several times this season. However, it's hard to back against the home side and with so much at stake, their greater experience should help them take a step nearer to a return to the top flight.