Leaney shot a final round 67 for a 72-hole aggregate of 271, 17 under par, and was the only man in the field to break 70 in all four rounds.
It was the biggest win on the European Tour since Nick Price won the Dimension Data Pro-Am by eight shots from David Frost in Sun City, South Africa, in February last year.
Karlsson shot 71 for 279. His fellow Swede Mathias Gronberg was third on 282.
Ricardo Gonzalez kept the Kenya Open title in Argentinian hands when he beat the local hero Jacob Okello at the third hole of a sudden death play-off in Nairobi yesterday.
Gonzalez and Okello had compiled closing rounds of 69 to finish on 12- under-par 272, three ahead of Mark Litton, of Wales, and England's Warren Bennett.
Both had pars at the first extra hole, the short 13th, and had birdie fours at the 18th. But back at the 150-yard 13th, Gonzalez sealed victory with a par to Okello's bogey after both missed the green.
In Florida, Colin Montgomerie remained among the leading pack at the Honda Classic after shooting his third consecutive sub-par round.
The Scot is one of eight players tied for fifth after a 71 left him on seven under for the Coral Springs event on Saturday. Germany's Bernhard Langer is another on 209 after recording a third-round 70.
The American Mark Calcavecchia heads the field on 205 after adding a 68 to his earlier rounds of 70 and 67. He is one shot clear of Fiji's Vijay Singh (68) and two ahead of Tommy Tolles (65) and Kevin Sutherland (70).
"I should have birdied 13 or 14," Calcavecchia said. "The birdie at 12 was an opportunity to pull away from the field. But I'm not going to look ahead."
"It's easier to hit certain shots when you're ahead than when you're around the cut," he added. "I've learned no lead is safe. They can disappear quicker than you think."
Jeff Maggert, who led by a stroke when the day began in search of his second PGA title, faded to 211 with a 76. Tom Watson started early and had a 67 to get to 210, along with Mark O'Meara and Craig Stadler. John Daly bounced back from a 76 for a 68 and was at four under, on 212.Reuse content