The performance, and the scoreline, lacked the emphatic nature of late, and for a time it seemed as though the home side would struggle to overcome their own hesitancy. But Rangers found a way to progress, and sometimes that has to be enough.
Manager Ally McCoist expressed his satisfaction afterwards, although the description of it as "a solid performance" was identifying the best feature of the display. Although Rangers dominated most of the possession, they did not generate a slew of chances. Asked about the potential of re-signing Kenny Miller, McCoist said he was keen, although the striker has agreed an extension to his Vancouver Whitecaps contact until next June.
"Kenny is one who would interest me," said McCoist. "If there was an opportunity to get Kenny, I wouldn't be doing my job if I didn't explore that. I haven't spoken to Kenny. But I wouldn't rule it out if that was a possibility. I will be making enquiries in the next 24 hours or so. I don't know if Kenny would want to come, I don't know if we can afford him. There are millions of questions."
A small crowd contributed to the muted sense of occasion. There ought to have been no excuse for a laboured Rangers performance, since the team was only denied the services of only two of the players - Nicky Law and Jon Daly - who have contributed to recent impressive results. The hosts' XI was still capable of a dynamic, purposeful display. Berwick, after all, remain in the bottom flight of Scottish football, and lost twice in the league at Ibrox last season. They set out to be dogged, but the mundane nature of Rangers' display was mostly the result of their own efforts.
David Templeton, making only his second start of the term, endured one of those games when his intentions did not match his actions. He was not alone, and there was a lack of willingness to commit to ambitious passages of play. Few midfielders, for instance, were prepared to carry the ball upfield and force Berwick players to move out of position. Rangers did not attack with enough pace or verve.
Lee Wallace did create one effort, with a ball into the left channel for Andy Little to chase, but the striker's first-time effort hit the midriff of Paul Grant, the Berwick goalkeeper. Rangers generated consternation mostly, although Little did almost score when he beat Grant to Lewis Macleod's pass, but his nick on the ball did not carry enough power to send it over the line and Michael Dunlop raced back to clear.
Rangers had to respond to their circumstances, and Sebastien Faure almost provided the decisiveness needed just after the interval with a volley that Grant tipped over. The effort roused the crowd, but it took a substitution to alter the home side's fortunes. Barrie McKay scored with his first touch after coming on, when he chased down a Templeton through ball and slid a shot past Grant.
Berwick might have been irked by their moment of insecurity. They dwelled upon it, though, since Little was left unmarked two minutes later and firmly headed Robbie Crawford's cross into the net. McKay should even have added a third, but lifted his shot over from a promising position.
The scoreline ought to have placated the home fans, but instead it allowed the singing section in the corner of the Broomloan Stand to turn their attention to the directors. They sang for the board to be sacked, and about the waste of money raised in last year's share issue. The silence of the rest of the stadium amplified the words, and it was a further reminder that an able enough victory in a low-key cup tie cannot divert from the off-field issues at Ibrox.
"We want to win this cup," McCoist insisted. "We want to win every competition we are in, but it will be tough against Queen of the South [in the next round]."