After a laboured opening from the hosts a quickfire double from Jason Cummings and Lewis Stevenson put Alan Stubbs’ men firmly in control.
The victory was secured in the second half when substitute Sam Stanton made an immediate impact to add a third before Liam Fontaine bulleted a header past goalkeeper William Bald to complete the scoring.
“I thought we were professional. We can give teams problems, we can be good at times but today was about making sure we were in the hat,” Hibs boss Stubbs told Sky Sports.
“I’m delighted from that point of view, but we’re not just going to Hampden for a day out.”
Stevenson played an important part in Hibs’ win, setting up Cummings for his goal before getting on the score sheet himself after a strong run into the box, paving the way for Hibs to seal a last-four spot.
“We created a few chances, it was an open game but the main thing was we got the job done but I don’t think it was as comfortable as the scoreline suggested,” he said.
“I’m really enjoying this season and hopefully we can get some success in the league and the Cup but there is a long way to go.”
Berwick boss Colin Cameron said: “The effort was there for everyone to see I thought we worked extremely hard.
“I thought we made a decent start but to lose two goals so quickly kind of knocked the stuffing out of us.”