Nevertheless, the victory will have done confidence no harm at all after the loss to Inverness on Wednesday that knocked Gers from the top of the SPL.
Steven Whittaker, Kyle Lafferty, Steven Davis and Aaron – in his first start for the club – all struck as the side cantered into the last four after an awkward start.
And the result takes the Light Blues’ goals tally against the Lanarkshire side up to an impressive 18 goals in five outings.
Walter Smith had been unhappy with the manner of the midweek defeat to Caley Jags, a game in which Rangers had plenty of possession but did little with it.
His team selection reflected his mood and four players dropped from of the starting line-up against an under-strength Accies side.
Out went Kirk Broadfoot and John Fleck altogether, while Kris Boyd and Mo Edu took seats on the bench.
Starting in their places were Whittaker, Aaron, Lafferty and, encouragingly ahead of next weekend’s League Cup final with Celtic, Pedro Mendes.
With more than 20,000 empty seats at Ibrox, it wasn’t too surprising that it was a low-key start to the game rather the pulsating match those who did turn up had hoped for.
But it didn’t take long for an atmosphere to build, with Whittaker marking his return to the team with his second goal of the season.
It was an excellent strike, with the full-back cutting in from the right past one man, taking the long way round a second and firing low past Tomas Cerny at the near post.
Rangers tried to build on their lead, with Madjid Bougherra having the best of their opportunities to extend the advantage.
But what followed next certainly wasn’t on the script as Hamilton levelled after 25 minutes.
James McCarthy crossed from the right and when Allan McGregor came to gather, he found a ruck of bodies in his way and couldn’t get anywhere near the ball.
Although it bounced off a head and away from goal, it landed at the feet of former Celtic midfielder Rocco Quinn and he drilled home from 12 yards to make it 1-1.
With the onus on Gers to come back at their opponents, they pressed again and were ahead once more just nine minutes later.
The build-up to the goal was odd, with Aaron doing well to get into space then passing 30 yards back downfield to Hamilton, who succeeded only in giving it away again.
Whittaker eventually swung back into the danger zone and when Kenny Miller met his cross, he set up Lafferty and the big striker rounded Cerny to score.
Finding themselves back in front, Rangers almost added a third thanks to some brilliant work by Sasa Papac down the left.
He did well to take the ball around Paul McGowan and when his cross was deflected and looped into the box, Miller was there to touch it on.
The Scotland star’s pass presented Lafferty with a chance to claim his second of the day but he just failed to connect inches from the line.
While he missed out, Aaron was more successful from the penalty spot on the stroke of half-time – if only just.
Gers won their spot kick with a good counter-attacking move that involved Davis then Miller, who was brought down by recently-introduced substitute Chris Swailes.
Miller handed responsibility for the penalty to Aaron but his attempt from 12 yards was poor and saved by Cerny.
Linesman Steve Pullar was quick to flag for an encroachment though and after the keeper was ruled to have come off his line too early, the chance to shoot again was given.
This time Aaron made no mistake, even if the retake was straight down the middle and close to coming off Cerny again.
The second half began badly for Hamilton who, after losing two players to injuries in the first period, lost a third in David Elebert at the break.
Soon after the restart, Offiong made it four after a collision with Whittaker and that left the visitors a man short.
Accies were quickly exposed and Davis made it 4-1 with an excellent strike, although he was given far more room than he should have been to score.
The Northern Ireland star picked up the ball on the right flank and charged forward when his opponents gave him the space to.
He quickly cut into the box and shimmied past his man before sliding in with his left foot from 10 yards.
From there, the game became something akin to a training exercise as the hosts seemed content with the size of their lead and the visitors looked to prevent further damage.
There was one moment of concern as Bougherra limped off and had to be replaced by the returning Lee McCulloch.
But home supporters were soon smiling again as Lafferty got on the end of a fine move instigated by Davis to make it 5-1 with 10 minutes to go.
That put the seal on a good win and now Rangers will play their semi tie on the weekend of April 25/26.