Hayley Lauder fired against a Hibs post and City’s pressure told when Shine finished off the underside of the crossbar before the break.
Shine’s second and third came late on, both left-foot strikes.
Hibs miss out on a sixth tournament win, having last won the Scottish Cup in 2010 and also finished runners-up to City in the Premier League and League Cup this year.
City enjoyed most of the possession and territory amid wet and windy conditions in Edinburgh.
Douglas girl Shine in particular troubled the Hibs defence and always looked the most likely to find the net.
Scotland international Lauder’s long-range shot smacked the post as City’s pressure built.
The opener came when Emma Brownlie was caught in possession in the right-back position and the ball ran loose to Shine, who stylishly lifted the ball over goalkeeper Jenna Fife.
Another effort from Glasgow’s Cuthbert tested Hibs keeper Fife but the second goal did arrive when Shine raced beyond the Hibs defence and finished clinically.
It was a similar story moments later as Shine capitalised on a slip by the Hibs defence to go through and beat Fife again.