McGinn stuck after just four minutes when he took a Stephen Hughes pass in his stride and nutmegged Ross Barbour before curling the ball past Cammy Bell.
Aberdeen should have doubled their advantage when Jonny Hayes led a counter-attack and found Scott Vernon at the near post but the big striker missed the ball completely as he tried to shoot.
Killie finally created an opening when Joe Shaughnessy’s slip allowed Paul Heffernan to set up Chris Johnston, and his shot parried by Jamie Langfield before the danger was cleared.
After the break Shaughnessy made a forceful run into the box to create a chance for McGinn but this time the Irishman shot straight at keeper Bell.
Vernon then had a deflected shot that fell kindly for McGinn, but with the goal at his mercy he again shot straight at Bell, and moments later the in-form winger sent a shot just past the upright.
Ryan Jack forced Bell into another save and Josh Magennis fluffed a late effort when he drove a shot into the ground from inside the box.