A double from the excellent Vladimir Weiss and Steven Whittaker’s penalty had the SPL champions on easy street at the midway point of their clash with Accies at Ibrox.
Maurice Edu then grabbed a fourth goal in a much quieter second period to give Walter Smith’s men an emphatic victory.
There was no return to action for striker Nikica Jelavic as he sat on the bench as an unused substitute for the whole 90 minutes with the Lanarkshire team.
That aside, it was an afternoon of positives for the Light Blues as they bounced back from their derby defeat well in their first league outing since losing to Celtic.
There weren’t too many surprises in the home starting line up, with Kenny Miller restored to the first XI after he missed the Scottish Cup tie with Kilmarnock.
Weiss also came in as Steven Naismith, a pre-match doubt with a slight hamstring strain, was left out as a precaution.
The champions had been impressive against Killie and were keen to make as bright a start as they had in that game.
But while Miller had made a couple of openings for himself early on, he couldn’t find the target as Accies got back in numbers.
Lee McCulloch, having opened his account for the season in his previous outing, might have had more luck had his drive from 25 yards not been deflected away for a corner.
Weiss was causing problems for the away side on a weather-beaten surface with his tricky feet and he drew a series of fouls from the Lanarkshire team.
One of them presented Steven Davis with a great chance and with a long-range curling free kick, he was only inches away from breaking the deadlock with a terrific effort.
Hamilton’s forays upfield were few and far between, with Grant Gillespie having a go from distance but succeeding only in firing well over the upright.
That aside, it was all Rangers in the opening quarter hour and Davis again could have scored after some intelligent play but he dragged his low shot across goal just wide.
Weiss also had a good opportunity and after some last-gasp intervention his eventual shot was helped behind for a corner.
For all their patient build up, the Light Blues hadn’t really tested away keeper Tomas Cerny yet.
But after Whittaker fed Madjid Bougherra and he cut back to McCulloch, the Scotland star was expertly denied by the Czech.
Cerny could do nothing moments later as Davis headed beyond him after good approach work by Weiss and Jamie Ness.
Unfortunately for the Northern Ireland midfielder, his attempt dropped the wrong side of the upright but a goal was certainly coming.
And on 24 minutes, with Ness teeing him up, Weiss smashed his side ahead with a stunning right-footed drive from fully 30 yards.
It wasn’t long before it was 2-0, with Weiss again at the thick of things as he duped debut defender Michael Devlin into a clumsy challenge just inside the area.
Referee Brian Winter was left in no doubt and pointed to the penalty spot, with Whittaker stepping up to fire in his second strike of the season.
Gers were in the mood and Davis almost made it three, with another block and a fingertip stop from Cerny all that stopped him.
Lafferty too did his best to strike following a lay off from Miller but his placed attempt was helped away before a header seconds after was turned over.
It would almost have been an injustice if the hosts didn’t extend their lead further before the break and they weren’t to be denied.
Weiss was having a good afternoon and after he found himself chopped down by Gillespie, it was the Slovakian who made it 3-0 on the brink of half time.
He took a curling free kick and although Miller darted clear of the last man to try to flick in, both he and Cerny missed the ball and it trundled inside the far post.
With such a commanding lead at the midway point, it wasn’t the biggest shock that Rangers began the second period with less tempo than they had had previously.
Even so, they continued to dictate play and both Davis and Lafferty were unlucky to see themselves denied spots on the scoresheet.
Miller, who was having a relatively quiet game by his standards, also headed over from a hanging Bougherra cross.
With his team in total control, manager Smith took his chance to make a couple of early substitutions.
Off came Davis and Weiss, with Edu coming on to continue building fitness after a knee injury and Gregg Wylde also getting another run out.
It was the teenage winger who made the more immediate impact, setting up McCulloch and Lafferty for missed opportunities.
With the game heading towards the 70-minute mark, fans were beginning to anticipate the introduction of Jelavic for the first time since October.
But an injury suffered by Sasa Papac meant he was to be denied a return, with Foster coming on for the Bosnian instead.
The match was very quickly losing the rhythm it had in an entertaining opening period and it rapidly took on the feel of a training game.
But Edu sparked it into life again eight minutes from the end when the ball sat up for him kindly in the box and he rammed in a well-struck fourth goal with his left foot.
Despite the fact Gers had clearly taken their foot off the gas in the latter stages, they were worthy of that size of lead.
But with time ticking down, they couldn’t add to it again – with Lafferty hitting the bar – though Smith will be happy enough with the final score.