The 29-year-old Price could not match his first-round mauling of Audley Harrison the last time out in October as he adjusted to Skelton's rugged charges and spoiling tactics.
But after edging the opening round, the undefeated Liverpudlian found the opening he was looking for and dropped the 45-year-old to his knees with a vicious pair of left hooks to the liver.
Skelton's corner threw in the towel almost immediately, but the ten count was registered by the referee anyway and Skelton did not rise.
Price moves his unblemished professional fight record to 15-0 with his 13th knockout, and Frank Maloney hinted afterward that his next opponent would be named very soon with a view to a February bout.
"We hope to name an American opponent for Price within the next 24 hours and that should go down in February," Maloney said.
When asked who would be next after that, Maloney suggested that they had offered Tyson Fury £650,000 to accept an all-British summer showdown, while Dereck Chisora's name was also brought up.
Price said of his latest conquest: "Matt put it on me straight away, he took me by surprise even though I knew what he was about.
"It was scrappy at times but I took him out in two rounds and nobody's done that sort of number on him yet."