After two probing opening rounds, 2012 Olympic super-heavyweight champion Joshua sent his opponent crashing to the canvas for his 18th win inside the distance in as many professional fights.
Molina, 34, clambered unsteadily back to his feet as the count reached eight, but the referee stepped in again to stop the fight after two minutes and two seconds of the round with a technical knockout declared.
The Texan had fought for the world title once before, losing to Deontay Wilder for the WBC belt in 2015.
Moments after the fight, promoter Eddie Hearn stepped into the ring to announce an April 29 bout against Ukrainian Klitschko at London's Wembley Stadium for the "unified heavyweight championship of the world".
Britain's Tyson Fury, who beat Klitschko in November 2015, vacated the WBA and WBO belts in October after having his licence suspended pending investigation of anti-doping and medical issues.
He had already been stripped of the IBF belt for not fighting a mandatory challenger.
"We move on to a bigger arena, more people can view it. This is the step up people have wanted. Klitschko wants his belts back, may the best man win," said Joshua after his second defence.
Klitschko, who had been watching ringside at the Manchester Arena, stepped through the ropes for some early eyeballing.
"He is the best man in the division and I believe this excitement speaks for itself. This is what the fans want and this fight must happen," said the 40-year-old.
"He was clear, clean and won by knockout and, as his next opponent, it was good I was here to observe it and make my notes."
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