Saints struck first at Rugby Park through 18-year-old John McGinn as the midfielder volleyed home his first senior goal from close range after 20 minutes.
Kris Boyd slotted past Samson five minutes later to level but Saints got themselves back on track for victory with Paul McGowan's spot-kick after Killie defender Lee Ashcroft felled the visitors' teenage striker Anton Brady.
Conor Newton added a third with a weak finish which should have been saved by home keeper Cammy Bell.
Shiels was happy with his players' display in spite of the result but was pleased to have confirmed the signing of Samson from their visitors.
He said: "It's great to have Craig at the club and hopefully we can move on and have a good season next year."