Paul Quinn converted an early penalty for the Shire but the treble from Little, a first Rangers goal on his first start from Francisco Sandaza and a late strike from Lee McCulloch secured a one-sided victory.
The Glasgow giants' first Third Division match at Ibrox attracted 49,118 supporters - one of biggest attendances in the United Kingdom this weekend.
Rangers chief executive Charles Green addressed fans ahead of kick-off, making reference to a campaign to sell out Scottish Premier League grounds last week.
He told the Ibrox crowd: "Never mind 'Sell-out Saturday' - this is 'Sold-out Saturday'. That's testament to the passion, loyalty and commitment shown by the Rangers support and we thank you all."
His comments were met with a loud cheer, as was Ian Black's name when the teams were read out, after the midfielder was jeered by Scotland fans when he made his international debut midweek.
Rangers made one change, with Sandaza replacing youngster Barrie McKay, who netted his first senior goal for the club in last week's draw at Peterhead.
Brazilian Emilson Cribari was named on the bench for the first time after being granted international clearance.
Once the action was under way, Rangers were stunned when East Stirling took the lead after just three minutes.
Referee Kevin Clancy pointed to the spot after Michael Herd went to ground under pressure from Carlos Bocanegra and Quinn kept his cool to lash past Neil Alexander.
Rangers immediately set about trying to haul themselves back into the game and Black saw his powerful long-ranger crash off the crossbar.
The home side continued to pile on the pressure and Sandaza set up Little for the shot in front of goal that goalkeeper Ryan McWilliams did well to block.
But he was plucking the ball out of the net with 15 minutes gone when Little collected from Black and slid the ball past McWilliams into the bottom corner.
There was a blow for Rangers when Dean Shiels limped out of the action clutching his right thigh after just 23 minutes, with McKay given the nod to replace him.
Sandaza should have had the net bulging with a left-foot volley but blasted high and wide from close-range.
Instead, the honours went to Little again, who threw himself in front of a Kirk Broadfoot cross and sent a diving header past the Shire keeper from six yards four minutes from half-time.
The Northern Ireland international should have claimed his third after the re-start when he met a Sandaza pass in plenty of space, took a touch, and then rifled well off-target.
Sandaza then turned provider for McCulloch, squaring into the path of the on-rushing utility man, only for his low drive to smack off the post.
Rangers were celebrating again after 63 minutes when Sandaza eventually stabbed home from close range in the packed goal-mouth after Broadfoot and Goian both had efforts blocked.
Little claimed his hat-trick 10 minutes later when he forced over the line after Sandaza's header was blocked by the keeper following excellent play by McKay.
With no way back for the visitors, Cribari was thrown into the action to make his debut with just over 10 minutes to go.
McCulloch then put the gloss on the win when he stroked home from a McKay cross in injury time.