David Templeton chips in along with Northern Irish forward to get the Third Division league leaders back on track after dropping two points at home to Elgin City last Saturday
Second-half strikes from Ross Gray and Fraser McLaren had got the Borders side back into the game, but they could not compete with the league leaders.
The home side made two changes from the Elgin game, with Dean Shiels and Francisco Sandaza coming in for Ian Black and Lee McCulloch, while Berwick made only one change from the team that won at home to East Stirling, with Douglas Brydon being replaced by Andy McLean.
Rangers opened the scoring early on as Sandaza made his way into the box and after a scramble, where the ball pinged about the Berwick area, it somehow found its way past two visiting defenders and into the path of Little, who from an acute angle managed to put the ball past Ian McCaldon and into the net.
Ally McCoist side looked to pile on the pressure and add to their goal tally but they found McCaldon in top form as the veteran stopper managed to make sure that Templeton could not find the net with a shot from the left wing.
The former Livingston keeper then defied Sandaza as the Rangers striker looked to get onto a cross from the left by Templeton, but McCaldon did well to make sure he got his body in the way and ensure the ball could not reach the Spaniard.
Rangers started the second half in superb style as Sandaza came from the middle of the park and played it towards the left wing and Templeton then whipped the ball with pace into the box for Little to volley home his second of the game.
The victory looked to be secured when Little made his way through the middle of the park before finding Sandaza wide on the right-hand side and his cross into the box found Templeton, who changed the position of his body to volley the ball beyond McCaldon and into the back of the net.
The visitors got a goal back as Dean Currie headed the ball to Kevin McDonald on the left hand side of the box and he found Gray, who had been on the park for less than a minute and he smashed the ball beyond Neil Alexander in the Rangers goal.
Berwick then reduced the deficit even further as McLaren got onto a corner from the right wing, rising above the Rangers defence to head the ball past Alexander and into the net.
But the two-goal advantage was restored moments later as Shiels found Little on the right-hand side and from the edge of the area the Northern Irish forward curled the ball beyond McCaldon to secure his hat-trick.
Rangers continued to pile forward but could not add more goals as they continue their march towards the Third Division title in some style.