David Templeton was also on the scoresheet, while Ross Gray and Fraser McLaren briefly provided hope of a comeback for the visitors.
Francisco Sandaza and Dean Shiels both started for Rangers, while captain Lee McCulloch missed out with an ankle injury and Ian Black was suspended.
Little was on the scoresheet when Rangers were fortunate to escape with a 1-1 draw at Shielfield and he was on target again in this match to open the scoring after just nine minutes.
Sandaza did well to force his way into the congested box but was unable to produce a clean shot and the ball fell for Little to stab over the line from an acute angle at close range.
Berwick's hopes of staging an Elgin style comeback began to fade when Little added to his earlier strike just two minutes after the restart when he volleyed home a Templeton cross from the left.
The former Hearts winger grabbed a goal of his own after 53 minutes. Little released Sandaza down the right flank and he whipped an inviting ball into the box where Templeton connected with an acrobatic volley, leaving Ian McCaldon with no chance.
There was a blow for Rangers when Chris Hegarty pulled up in the middle of the park and the defender was quickly replaced by Sebastien Faure.
But it was a Berwick substitute who had an immediate impact on the match.
Gray pulled a goal back for the visitors after 66 minutes when he lashed home from a Kevin McDonald cut-back with his first touch of the ball.
McLaren then dispatched a bullet header into the back of the net from a Lee Currie corner after 73 minutes to claim his second goal of the season against Rangers.
Just when a tense finale appeared to be on the cards for the home side, Little completed his hat-trick with a cool finish from the edge of the box a minute later, before Templeton struck the post late on.