After the high octane drama of their Premiership win over Celtic 19 days earlier, this was considerably more mundane fare for Steven Gerrard’s men.
But the primary objective of a place in Sunday’s fifth round draw was duly achieved courtesy of Scott Arfield’s opener just before half-time and a Jermain Defoe penalty midway through the second half.
There were only four survivors in Gerrard’s starting line-up from the side he deployed in the Old Firm victory at Celtic Park before the break with that afternoon’s match-winner Nikola Katic retaining his place along with Ryan Jack, Steven Davis and Joe Aribo.
Of those who were handed their opportunity to catch the manager’s eye, the greatest interest surrounded 18-year-old Nathan Patterson, who made his first-team debut at right-back.
Patterson was quick to display why he is rated so highly by Gerrard, showing poise and eye-catching technique as he stepped into the role vacated by injured captain James Tavernier.
The teenager created the first opportunity of a match, which saw Rangers forced to show patience and persistence to break down Stranraer’s robust 5-4-1 formation.
Patterson found space to whip over a fine cross in the ninth minute which Defoe might have done better than meet with a glancing header which sailed well wide.
Jordan Jones, making his first appearance since suffering a serious knee injury almost six months ago, was presented with the hosts’ next chance but headed Arfield’s cross over from close range.
Rangers were moving the ball around with precision but found the final incisive pass in Stranraer’s congested defensive third of the pitch elusive.
Jack, deputising as captain for Tavernier, tried to seize the initiative and saw a long-range shot deflected wide. The midfielder then got on the end of a neat move involving Andy Halliday and Defoe but saw his shot saved smartly by Max Currie at his right-hand post.
Joe Aribo and Defoe both saw efforts slide narrowly wide as Rangers tried to bring greater intensity to their work but Stranraer remained defiant and had little ambition to try to support lone striker Ryan Stevenson.
Another of their experienced former Hearts men, Jamie Hamill, pictured, picked up the first yellow card of the night for a nasty looking challenge which left Halliday in considerable discomfort.
Just as it seemed Stranraer would succeed in frustrating Rangers until the break, they were undone by a set piece in the 44th minute.
While no-one could dispute the goal was the least Rangers deserved for their complete dominance, there was an element of fortune involved. George Edmundson’s attempt to flick on a Steven Davis corner inadvertently knocked the ball into the path of Arfield, who beat Currie with a low left-foot shot from around eight yards.
Rangers almost doubled their lead in first-half stoppage time but Currie produced a fine save to keep out Katic’s close-range header from another Davis corner.
Patterson continued to impress, although a rare poor touch from the teenager saw him lunge into a challenge on Andy Stirling which earned him a booking. He quickly regained his composure and was denied a debut goal in the 57th minute when his rising shot from the edge of the penalty area was tipped over by Currie.
Jones, one of the fringe players in Gerrard’s squad who certainly failed to make the most of his chance to stake a claim for future involvement, was substituted just after the hour mark with Brandon Barker entering the fray.
Stranraer were visibly tiring, which was unsurprising in light of both the physical effort and concentration levels they had brought to their defensive gameplan.
They were finally breached again in the 66th minute when Adam Cummins found himself on the wrong side of Defoe in the box and brought the striker down with a weary challenge.
In what proved to be his last contribution before being replaced by Sheyi Ojo, Defoe took the penalty himself and sent Currie the wrong way to claim his 15th goal of the season.