Thornton travelled to a sunny, but blustery, Treaton Park looking to put the disappointment of their defeat at Dalkeith behind them.
And they began this Fife and Lothians cup-tie in determined fashion taking the lead in the 12th minute when Nathan Feeley netted from the edge of the box; his first in a Hibs' jersey.
They continued on the front foot playing some of their best stuff of the season and it was no real surprise when they doubled their lead in the 34th minute. Ryan Linton's free-kick from deep inside his own-half found Adam Drummond in the Star penalty box and he headed the ball into the path of Garry Thomson who netted from close range.
The home side made a better fist of things in the second-half but couldn't find a way past the Hibs' defence with Ryan Linton rarely called into action.
Late on, Daniel McNab received a second yellow but this made no difference to the outcome meaning that Thornton will now travel to Sauchie in the second round on a date to be advised.
SM Electrical Services (Fife) Hibs' Man of the Match: Ian Hepburn
Kennoway Star Hearts: Paterson, McGowan, Johnstone, Brewster, Doig, C.Gay, M.Gay, Young, Band, Rolland, Collins. Subs: Shaw, Newlands, Partridge, Muir.
Thornton Hibs: Linton, M.Robertson, D.McMillan, S.Drummond, Shields, A.Drummond, Keatings, Hepburn, Feeley, Thomson, McNab. Subs: Strachan, Coleman, Shanks, Forbes, Ireland.
Referee: Mr J.Bell