Two goals in either half ensured that there would be no upset at Easter Road as Hibs comfortably cruised past their Scottish League Two opponents.
Having started off second best, Berwick could have taken a surprise lead had Lewis Stevenson not been alert on the line to clear away a headed attempt.
Moments later, Jason Cummings edged Hibs ahead after latching onto a through ball and keeping his cool to slot home with 26 minutes on the clock.
Just two minutes had transpired before Stevenson doubled his side's tally as Berwick's resolve broke. He ran onto Dominique Malonga's pass to score and put the hosts in control.
Fraser Fyvie and Lee Currie saw chances come and go as both teams looked to find the third goal of the contest prior to the break, but it remained at 2-0 until after the hour mark when Sam Stanton killed off any hopes that the Black and Gold had of mounting a comeback by tucking away a rebound inside the area.
The fourth was added eight minutes from time by Liam Fontaine, who met a corner to fire Hibernian into a Hampden Park semi-final.