Leapai, the first Australian to fight for a world title at top weight in over a century, was a game challenger but no match for the massive Ukranian, who was making the 16th defence of his belts.
From the start, the champion was able to keep Leapai at bay with stinging left jabs, the smaller man proving far too static to work his way inside the Ukranian’s defence.
Leapai found himself on the seat of his pants two-thirds of the way through the first round and took a standing eight count, but there was some suggestion he had simply slipped.
Nevertheless, Klitschko continued to pick the challenger off with that accurate jab, winning each of the first four rounds easily.
After around a minute of the fifth, a wild swing from Leapai seemed to have connected with the champion, who briefly staggered across the ring, but replays suggest the connection was slight at best.
In response, Klitschko hit Leapai square-on with three straight jabs, then a left-right combination which sent the challenger to the canvas.
He was able to continue after a count, but the Ukranian gave him no respite, and another combination ended the fight with one minute remaining in the fifth.
Klitschko said in the ring subsequently that there were "no easy fights", but he would be hard-pushed to recall an easier one for him in his ten-year reign as champion.
Bermane Stiverne and Chris Arreola, who fight in two weeks for the WBC world title until recently held by Wlad's big brother Vitali, will have been watching for signs of weakness in the champion, but in reality Leapai was not the man to tease them out.
The winner of the summer bout between British fighters Tyson Fury and Dereck Chisora may offer an alternative follow-up fight for the champion, but his management may be wary of Fury in particular - one of the few heavyweights fighting at world level who can match Klitschko for size.