David Templeton was also on the scoresheet, while Ross Gray and Fraser McLaren briefly provided hope of a comeback for the visitors.
Rangers may now be well on course for the title but might not earn promotion to a higher division if reconstruction plans for a 12-12-18 league format are implemented for next season.
Such a scenario would leave the Light Blues in the bottom tier for a second campaign and chief executive Charles Green has said he wants Rangers to quit Scottish football if the proposals are rubber-stamped.
In an ironic twist, in the week where debate over cross-border leagues was resurrected, the Glasgow giants played host to an English-based club in a league match for the first time.
There was another first in the shape of a female assistant referee at Ibrox, with Lorraine Clark tasked with running the line.
Rangers made two changes from the side who were held to a draw at the same venue by Elgin City last week.
Francisco Sandaza and Dean Shiels both started, 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 when the two sides met earlier in the season.
And the Northern Ireland international 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.
There was a chance for Sandaza to leave the net bulging when he eased past Devon Jacobs only to see his strike pushed to safety by goalkeeper Ian McCaldon.
The Spanish striker - who had a lengthy spell out of action recently with a fractured cheekbone - was desperate to add to his solitary goal this season.
But Sandaza was again left frustrated when he just failed to connect with a teasing cross from Templeton at the back post and stab home.
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 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 visitors after 66 minutes when he lashed home from a Kevin McDonald cut-back with his first touch of the ball, moments after being thrown into the action.
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.