Kenny Miller's seventh goal of the season gave Rangers a last-minute win over a battling Hamilton Accies side.
Nikica Jelavic headed home his first Rangers goal early on and the visitors maintained their lead until the break.
Accies had competed well in the opening period and were rewarded for their efforts when Madjid Bougherra's own goal levelled matters.
But substitute Miller's lob restored the champions' lead and their 100% Scottish Premier League record.
Watched by Manchester United scout Martin Ferguson, the match was Rangers' last before beginning their Champions League campaign at Old Trafford on Tuesday, while Hamilton were looking to build on their recent win over Inverness.
Referee Alan Muir ignored early penalty claims from the home crowd after Nigel Hasselbaink was squeezed out by David Weir and Sasa Papac just inside the area.
Jelavic was making his full debut for the Ibrox side and, within six minutes, the Croatian had found the net after bulleting Kyle Lafferty's teasing cross into the net.
Hamilton rallied and came close to an equaliser twice in quick succession.
First, Marco Paixao's curling shot was tipped over by Allan McGregor and the goalkeeper then held a deflected shot by Jon Routledge.
Marco Paixao continued to cause Rangers problems and flashed an effort wide after cutting in from the left.
Jelavic turned provider with a low cross across the Accies box, but strike partner James Beattie could not get the vital touch.
A series of lofted balls into the Rangers box ended with Simon Mensing flicking a backwards header towards goal, but McGregor was on hand to claim.
Jelavic notched his first Rangers goal in the first half
Jelavic shot wide via a deflection on the half-hour mark shortly before being caught late by Jim Goodwin, resulting in a booking for the Hamilton debutant.
Cerny palmed an awkward deflected shot by Jelavic into the path of Beattie, but the Englishman could not turn his rebound into the net.
Kirk Broadfoot limped off shortly before the break after failing to recover from an earlier knock and Ricky Foster made his first Rangers appearance after joining on loan from Aberdeen.
The versatile defender was caught cold when his tame headed clearance let Hasselbaink in on goal and McGregor was required to make a last-ditch save to deny the former PSV Eindhoven player.
Hamilton got themselves level 11 minutes after the break when Bougherra turned Marco Paixao's cross into his own net.
Steven Naismith's powerful drive was beaten out by Cerny as Rangers tried to regain the advantage.
Accies continued to pose a threat on the break and one such attack saw Flavio Paixao's curling shot deflect just wide of the target.
Top scorer Miller was introduced from the Rangers bench as Lafferty was withdrawn and the striker set up Jelavic with a neat lay-off, but Cerny saved well.
Steven Davis dragged a shot wide from distance as Rangers pressed for a late leveller.
But Miller did find the net after latching on to fellow substitute Lee McCulloch's intelligent through ball, despite Cerny getting a hand to the shot.
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