The American superstar came from behind to close the show in round eight with two brutal left hands.
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Davis’ first uppercut set up the finishing blow to land Martin flat on his back and out for the count.
The WBA champion bounced back after 14 months out the ring amid legal troubles to claw back his 27th knockout in 29 unbeaten fights.
Davis, 29, said: “Just a little rusty but I’m back.
“A couple of rounds I feel I didn’t warm up completely like how I wanted to but I did warm up and got caught as the fight was going on. But it’s okay, no excuses.”
Martin – who began boxing aged 18 after ditching his NFL dreams – started the quicker to draw up an early lead.
Davis – who walked out to a Ghostbusters theme – was on the front foot throughout but walked into jabs, left hands and combinations.
But bit by bit the man affectionately known as Tank crept ever closer to landing the finishing blow.
In round seven, the writing appeared on the wall as Martin’s firepower dwindled and his responses dramatically dipped.
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Davis trapped Martin into the corner and unloaded with left hands as the challenger no longer was able to return with damaging counters.
And in round eight, Davis backed Martin into the ropes allowing his trademark left uppercut to stun the Texan.
In a flash, Davis followed up to nail a left hand into a defenceless Martin.
The referee began counting but the champ was already celebrating on the top rope.
Eventually, Martin, 29, was counted out and Davis declared the winner to mark a sensational return over a year after beating Ryan Garcia, 25.
He added: “I’ve been training since I was seven-years-old, competing since I was eight so it’s like second nature.
“It’s about staying focussed. Make sure my minds on the goal and it’s always to come out on top.”
Martin, beaten for the first time, said: “I felt like in the beginning I was in control and then got a little too comfortable.
“I got caught chilling on the ropes, trying to find that bigger shot it wasn’t presenting itself.
“I stopped doing my movement and once I stopped doing my movement he was able to land more shots.
“Once I stopped doing my thing he got off more shots on me.”
Davis now has the likes of Vasyl Lomachenko, Shakur Stevenson and a rematch with Isaac Pitbull Cruz in his sights.
He added: “All them guys are on my radar.”