But he came off the bench with 18 minutes left and grabbed the goal that counted 60 seconds from the end to clinch a crucial victory.
Nikica Jelavic also marked his full debut with a goal inside five minutes and not even Madjid Bougherra’s own goal could stop the champions.
Now it’s next stop Old Trafford – and if this game proves anything it’s that Gers will show plenty of fight and desire against Sir Alex Ferguson’s Red Devils.
This certainly wasn’t an impressive victory by any means but as they’ve done so often in the past, the title holders ground out the outcome they needed.
Smith took the opportunity to rotate players three days before the trip south and Lee McCulloch and Vladimir Weiss also dropped to the bench.
Steven Whittaker wasn’t risked after a calf injury.and in came Kirk Broadfoot, Maurice Edu, Kyle Lafferty and new signing Jelavic.
Rangers were wearing their new all-black kit for the first time at New Douglas Park and looked imposing in the change outfit.
And they very nearly went in front in the opening stages when Steven Naismith threaded the ball through for Jelavic.
James Beattie was offside when the ball was played and he knew it so he held back and allowed the Croatian striker to charge through.
Whether he had also strayed past the last defender too early or not was unclear but the flag went up and Tomas Cerny saved in any case.
At the other end, Nigel Hasselbaink had a weak penalty claim waved away and with that, the stage was set for Jelavic to break his duck.
His goal was a simple close-range header but it all came about after great work by Lafferty on the left wing.
He received the ball from Sasa Papac and stepped away from one man before bursting past another then surging beyond a third and playing himself down the wing.
When he swung his cross into the middle, it was perfect for Jelavic to rise and nod in from six yards to give the Light Blues an early lead.
The 25-year-old wheeled away and punched the air in delight – and the away support was every bit as ecstatic as they celebrated the early opener.
Hamilton’s response was slow but when it came, it took a fantastic save from Allan McGregor to keep out Marco Paixao’s curler.
Jon Routledge then had a go from the resulting corner but his low drive was deflected and comfortably gathered by the Scotland keeper.
Paixao tried again as Accies broke forward with pace from midfield but on this occasion he was off target.
A moment of real class from Jelavic saw him twist past his marker into the box and a pinpoint pass across the area gave Beattie a chance to net.
But he was unlucky to see his effort roll off target before Lafferty’s cutback was smothered by Cerny with others lurking in the area waiting to pounce.
Jelavic was in the mood and on the half-hour mark a good passing move allowed Edu to set him up, with a block tackle proving crucial in sending his effort just wide.
A long throw into the area from Edu was flicked on by Lafferty and gave Naismith a chance as the visitors cranked up the pressure.
But Cerny came out to gather well at a time when the champions were starting to look really threatening on a regular basis for the first time in the game.
Jelavic went close again as he tried to pick his spot in the far corner and when Cerny only parried, Beattie was always struggling to turn the rebound in.
Broadfoot had taken a knock earlier in the game and fresh from a recent ankle injury, he had struggled to shake it off.
That meant new loan signing Richard Foster was introduced as his replacement three minutes before the break.
Almost instantly Hamilton were level after the on-loan Aberdeen man lost possession but McGregor spread himself superbly to deny Nigel Hasselbaink.
That was the last real action of the first period, with the SPL champions going into the break still leading.
And although their lead was a very narrow one, Smith decided not to make any changes to his team at the break having been satisfied with their initial showing.
Although Rangers had more of the ball after the restart, they were pegged back 10 minutes in.
Paixao latched on to a long raking cross on the left side of the penalty area but there seemed to be little danger at that stage.
Yet when he swung across the face of goal, Bougherra’s attempted clearance only diverted the ball into the net to make it 1-1.
With that, Hamilton’s tails were up and with a noisy home support behind them, they set about trying to go in front themselves.
But it was Gers who came closest to scoring next when an injured Naismith was able to get a shot on goal and Cerny palmed it on to the bar then behind.
Hamilton also tried their luck, with Flavio Paixao finishing a fine flowing break upfield by just missing the top corner.
Going into the final quarter of the match, the visitors were looking a bit flat and McCulloch was brought on for Beattie to give them a more solid look.
Miller then entered the fray for Lafferty and he almost made an immediate impact as he teed up Jelavic.
His smart backheel opened things up for the Croat, who should probably have better and shot straight at Cerny with the goal gaping.
Steven Davis drove from distance as the Ibrox outfit began to run out of ideas with time running out and his attempt flashed over.
There were just minutes remaining and Rangers needed a lifeline if they were to keep up their 100 per cent start to the SPL.
And with just one minute to go it finally came – with that man Miller grabbing the glory in fine style.
McCulloch did really well to charge in and win the ball, playing a defence-splitter through to his international team-mate.
Miller then picked his spot with a deft lob and although Cerny got a hand to it, he couldn’t stop the ball dropping in.
It was a goal fit to win any game and it was enough to help the Light Blues sneak three points at the end of a tough afternoon in Lanarkshire.