The first warning signs came inside the opening five minutes as both Kyle Lafferty and Mitch Pinnock had headers off target.
The breakthrough came for the Ayrshire side on 36 minutes when Jonathan Tiffoney was ruled to have pushed over Lafferty after a long ball into the Stenny penalty area.
The former Rangers and Hearts striker stepped up himself and swept the ball low to Paddy Martin's right with the on loan Hibs keeper guessing the right way but unable to get a hand on the well placed spot kick.
Killie scored a second just before half time as Rory McKenzie set up Lafferty who fired it past Martin from 18 yards.
The Premiership sides domination continued in the second half when a deep cross by Pinnock was met by the late run of Lafferty who saw a free header come back off the post.
The Northern Irish international didn't have to wait long to complete his hat-trick though as Chris Burke drove past Callum Yeats and into the box with ease on 55 minutes before squaring the ball to Lafferty who tapped in to an empty net from close range.
Chris McQueen prevented it from being 4-0 on 57 minutes when he cleared a Pinnock shot off the line after the winger got on the end of a long ball over the top and slotted past Martin.
Martin made a good save to deny Youssouf Mulumbu from a free kick as he clawed the ball away before it could fly into the top corner on 71 minutes.
Stenny pushed to find a consolation and on 84 minutes, substitute Thomas Halleran did well to keep a hold of the ball in the middle of the park before driving forward and unleashing a shot from distance but it was comfortably held by Colin Doyle.
The Premiership side caught Stenny on the break for their fourth on 86 minutes when a long ball up the park found Aaron Tshibola who played in George Oakley and the former Hamilton striker drove in to the box and calmly slotted it past Martin to finish the scoring on 86 minutes.