Late goals provided a flourish, but Rangers were most reliant on a sense of bloodymindedness.

For periods they were not the dominant side, and Queen of the South could regret some spurned chances, but the Ibrox side prevailed. That is a form of progress for a team that has previously been mentally frail, and a Ramsdens Cup semi-final was the reward for such perseverance. "We were resilient," said manager Ally McCoist. "They handled the surface a lot better than we did. But as a team we looked solid. They put us under a lot of pressure, but we dealt with it really well."

Rangers were seeking redemption. Queens won on penalties in this competition last season, in a game at Ibrox that exposed the psychological vulnerability of the team that emerged from a traumatic summer. Only four members of the starting line-up last night were at Rangers 12 months ago, so this quarter-final tie was an opportunity to emphasise that improvements had been made.

Spirits have been raised in recent weeks, even if a series of emphatic victories were not always accurate reflections of the balance of the games themselves. Yet Rangers acted as though initially alarmed. Richard Foster ought to have been decisive in clearing the ball from the edge of his penalty area, but instead sliced it over his own crossbar. From the resulting corner, Jon Daly and Bilel Mohsni collided with each other as they both tried to head clear.

Misunderstandings are inevitable as players become accustomed to each other, but it did not need to be debilitating. No sense of anxiety was allowed to settle, after all, when Rangers immediately established a lead. Their first attack ended with Arnold Peralta's corner being headed back across goal by Lee McCulloch, and Mohsni turning it into the net from close range.

The promise, then, was of a dominant performance. Steven Smith was tigerish in midfield - and one cross-field pass to Daly was perfectly executed, but the striker volleyed over - while Nicky Law was determined to be an influential figure. The chasing and the harrying was relentless, but it didn't bring command. Senses were still frayed, and Cammy Bell's heavy touch on a pass back sent the ball straight to Iain Russell, who squared it to Derek Lyle. With the Rangers goalkeeper scrambling to get back to his line, Lyle tried to dink a shot into the empty net, but Mohsni's sliding block saved the visitors.

Last-ditch defending tends to rouse fans, but it is also indicative of slackness. Mohsni rescued one situation, but was then culpable as Michael Paton made room to cross, but Lyle's header was plucked out of the air by Bell. It was telling that Rangers used the half-time interval to switch to a 4-1-4-1 formation, bringing Little back into midfield and leaving Daly to lead the attack on his own.

The change allowed the visitors to match up to Queens' three central midfielders, although it was the home side whose play was often slicker and more composed. The goalkeeper, Calum Antell, preferred to roll the ball out to his centre-backs than launch it upfield, and one impressive spell of dynamic passing ended with Ian McShane sending the ball flashing across the face of Bell's goal.

Queens might then have forced some doubt into the minds of the Rangers players, since the visitors were seeking containment. Perhaps the home side were susceptible to anxiety too, though; Chris Higgins was rash as he sought to win the ball from Smith and fouled the midifelder instead. Having been booked in the first-half for dissent, he was dismissed for his lack of composure. "The sending off was pivotal," said Jim McIntyre, the Queens manager. "It was really damage limitation after that. But I was proud of my players. Rangers knew they were in a game."

The punishment was not confined to giving Rangers an advantage in terms of players, since Law then flighted the free kick into the area and Daly glanced beyond Antell. Eight minutes later, McCulloch scored with another header, from Robbie Crawford's corner, to secure a scoreline that was more emphatic than the display that delivered it.

Afterwards, McCoist also revealed that he will speak to Marius Zaliukas, the former Hearts defender, before the end of the week about the contract he has been offered by the Ibrox side.