Both teams found the strong wind difficult to deal with but it was Thornton Hibs who coped better, a goal in each half earning them the three points in the first game played in their League Cup section.
The Hibs came close to snatching an early opener with Adam Drummond heading Max Coleman's corner-kick just over and then Ben Anthony saw his shot on the turn saved by the foot of Robbie Paterson.
Thornton took the lead in the 31st minute when Anthony's cross was head-flicked by Nathan Kiristino into the path of Matthew Robertson who nodded the ball home from close range.
Liam Craig came close twice to grabbing an equaliser before the first-half drew to a close.
On the hour mark, Nathan Doig headed Craig Johnstone's cross over its intended target and then Johnstone tried his luck with a powerful volley that was held by Ryan Linton.
The killer goal came in the 78th with Anthony again providing the cross. This time the ball fell at the feet of Daniel McNab who steadied himself before smashing the ball low past Paterson.
GI Joinery Hibs' Man of the Match: Ben Anthony
Thornton Hibs: Linton, Robertson, McMillan, A.Drummond, Shields, Orrock, Keatings, Coleman, Anthony, Thomson, McNab. Subs: Hepburn, Shanks, Millar, Kiristino, Ireland.
Kennoway Star Hearts: Paterson, Mair, Johnstone, Brewster, Doig, Young, Craig, Collins, Band, D.Muir, B.Rolland. Subs: Bryce, Watson, Bremner, Lindsay, Muir.
Referee: Mr A.Budd