Walter Smith made two changes to his side that beat Killie 3-1 at Ibrox last weekend.
With Pedro Mendes out with a thigh strain he gave Mo Edu his fourth start in all competitions – his second in the league – alongside skipper Barry Ferguson in the heart of midfield.
The gaffer also named Kyle Lafferty on the left side of midfield in place of John Fleck who was on the bench.
With Hamilton pushing for a top six slot this was always going to be a tricky test for the Gers who started the game positively.
It was evident from the first whistle that when defending the home side were sitting deep in a 4-5-1 formation but this would change immediately to a 4-4-2 when they had possession.
This, however, did little to stop Rangers in a first-half they dominated from start to finish.
After only two minutes Lafferty cut in from the left flank and his low shot across goal from 25 yards brought out a good save from Tomas Cerny.
This was a sign of things to come and only three minutes later Miller did well to create space on the left wing and his tempting cross was headed inches wide by Steven Davis.
Prior to the half-hour mark Boyd had a 20 yard free-kick blocked by the Hamilton wall and in the next attack he flicked the ball past Alex Neil inside the 18-yard box but the defender did well to recover and stop a certain goal.
The breakthrough finally arrived on 35 minutes and it was captain Barry Ferguson that hit the net with his first goal since May 7, 2008 against Motherwell at Ibrox.
Davis and Weir played a short corner and when the latter swung the ball in it was cleared out to Ferguson who drilled a terrific left-foot shot beyond Cerny from 20 yards.
Rangers could have doubled their advantage before the interval when Davis played in a terrific corner which Broadfoot won in the air.
The ball was heading goalwards but Miller decided to glance it on and it came off the underside of the bar before being cleared.
The second-half started in a similar manner to the first with Rangers attacking and Davis, in particular, pulling the strings in a Light Blue jersey.
As expected Hamilton came out fighting but Mensing showed a bit too much commitment on 52 minutes when he produced a crunching tackle on Edu which left the American lying in a heap on the half-way line.
With only one goal separating the teams with an hour gone the home support were still hoping their side could grab an equaliser and when Boyd saw a terrific chance saved by Cerny they were given another boost.
Reid was to make his third change of the game on 62 minutes when Kenny Deuchar replaced Martin Canning and the towering striker immediately moved up alongside Richard Offiong to add to Hamilton’s attacking threat.
Rangers remained the more dangerous of the two sides and on 70 minutes Boyd was hauled down 25 yards from goal but Davis’ tame free-kick was easily gathered by the impressive Cerny.
The free-kick was certainly debatable but the home support voiced their growing displeasure at referee Craig Thomson’s performance on the day.
Smith made his first change with 74 minutes gone with Steven Whittaker replacing Lafferty on the left side of midfield and straight away he was in the thick of the action.
Rangers, however, were making tough work of this short trip to New Douglas Park and when Davis squandered yet another chance having been one-on-one with Cerny there appeared to be growing concern on the visitor’s bench.
With time ticking down Alex Neil was booked for a terrible challenge on Steven Naismith, who had only just stepped on the pitch in place of Kenny Miller.
Barry Ferguson then received a yellow card for confronting the Hamilton midfielder in the flare-up that followed.
Davis was also to find his way in to the referee’s notebook for a late challenge which looked partly due to tiredness after yet another industrious display..
Hamilton have been given plenty of praise for there work-rate this season and that was certainly on show again today but Rangers were impressive and secured three crucial points and stay at the top of the SPL.
Star Man: Steven Davis – The Northern Ireland man was outstanding and deserved at least one goal for all his effort.