The Englishman was on target in each half while Manuel Pascali headed the second goal shortly after the break.
However, the visitors enjoyed plenty of possession and created a fair few chances themselves and also struck the woodwork through Ryan Stevenson’s long range effort late in the first half.
Home keeper Craig Samson made a superb double save while the game was still goalless, diving low to block a swerving Steven Lawless effort, before denying the follow-up from Kris Doolan.
Obadeyi broke the deadlock in the 25th minute with a stooping header into the bottom left-hand corner of the net from Ross Barbour’s cross.
Pascali nodded home the second from close range on 51 when he met Alexei Eremenko’s corner.
And six minutes later Obadeyi added a third with a low strike from outside the box, following another Eremenko assist.
Killie dominated the remainder of the match and could have added further goals with Eremenko, Sammy Clingan and Pascali all going close, while Christie Elliott had a late effort for Thistle.