After two cagey opening rounds, Davis landed a series of heavy shots that dropped Walsh to the canvas.
Walsh, 31, got to his feet but another hard left from Davis, 22, saw referee Michael Alexander step in.
Davis, who is promoted by former five-weight world champion Floyd Mayweather, is now unbeaten in 18 fights.
His latest knockout victory marks a successful first defence of the title he won by beating Jose Pedraza in January.
Earlier, Walsh's twin brother Ryan retained his British featherweight title against Marco McCullough.
Liam Walsh - unbeaten in 21 bouts - entered the contest having waited almost five years for a shot at a world title, after a car crash forced him to pull out of a scheduled meeting with Scotland's Ricky Burns for the WBO lightweight title in 2012.
Yet the Cromer-based fighter quickly found himself outclassed by the young American, who Mayweather calls the "future of boxing".
The first round was largely a stalemate, with Davis keeping Walsh at bay with the jab, before the Baltimore fighter - nicknamed 'Tank' - upped his speed and accuracy to land several blows with his left in the second.
He increased the power of those hits in the third round and continued to hurt Walsh with the left, eventually forcing the first knockdown.
Walsh raised his hands as he returned to his feet but lasted just four more seconds before Alexander waved off the contest to give Davis victory by technical knockout, despite the Englishman protesting against the decision.
"It was just a matter of time before I got him," said Davis.
"I used my boxing IQ and picked my shots - when I connected, I got him out of there."
Victory for the Walsh family earlier on the bill came when Ryan stopped Northern Ireland's McCullough in round 11.
McCullough, 27, battled bravely to stay in the contest but found himself pinned against the ropes by Walsh, with the referee stepping in as his hands dropped.
It is the third time Walsh has defended his British belt and extends his record to 22 wins, two losses and one draw.
Elsewhere, there was an impressive victory for 19-year-old heavyweight Daniel Dubois, who knocked out David Howe, 36, after only 40 seconds with a powerful right hand.
American Gervonta Davis defended his IBF super-featherweight title by stopping Britain's Liam Walsh in round three at London's Copper Box Arena.