McCulloch headed home Connor Young’s corner after just seven minutes before O'Connor converted a penalty shortly before the interval.
Killie had their chances and Hibs could have added to their tally, but will be happy enough with another three points and another clean sheet – their eleventh of the season.
Hibs started on the front foot, winning a corner early on which Young floated in towards the six-yard box where the arriving McCulloch was left unmarked and free to nod the hosts into the lead.
Killie could have levelled moments later after a quick break but Johnson was happy to see the ball out for a goal kick.
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O’Connor’s pace was causing the visitors problems and he delivered a wicked cross to strike partner Young, whose header had power but not accuracy as it dropped just wide of Aiden Glavin’s right-hand post after a quarter of an hour.
With 25 minutes on the clock Sean Clark wasn't far away with a powerful free kick and at the other end, Robbie Hamilton dragged a shot just wide of the far post from the edge of the box.
As half-time ticked closer, O’Connor carried the ball into the penalty area beore being clipped as he shaped to shoot. The striker dusted himself off and sent Glavin the wrong way from the spot to double Hibs’ advantage.
Malik Zaid might have made it three minutes later but he couldn't convert Young’s centre, while Glavin did well to thwart O’Connor in a one-on-one after the Hibs forward pounced on a short pass-back.
Killie came into the game more in the second half but were unable to really test Johnson. O’Connor had a couple of half-chances at the other end while Murray Aiken came close after a surging run from just inside his own half. Mack Weir’s glancing header from McCulloch’s bicycle-kick effort following a corner was well saved by Glavin, who also saved from substitute Ethan Laidlaw before pulling off a stunning one-handed stop to deny Young in injury time.
Hibs remain second in the table, two points off leaders Rangers with six games in hand.