The Briton successfully defended his IBF world heavyweight title for a second time with another brutal demonstration of his power-punching to claim an 18th stoppage win from as many professional bouts at the Manchester Arena.
Joshua forced the stoppage in two minutes, two seconds of the third round after first flooring American Molina with a right.
Klitschko, the former world No 1 who lost three titles on points to Joshua?s fellow Briton Tyson Fury last year, was ringside to check on Joshua and could not have failed to have been impressed.
Klitschko -- 41 in March -- and Joshua are being lined up to meet on April 29 at Wembley Stadium in London, and the Ukrainian will be a big step up in class to Molina.
"I was patient and we move on. This is not the end of the story,? said Joshua in the ring.
"You will realise what I?m all about now. Klitschko wants his belts back and may the best man win. I will worry about myself and training."
Klitschko then got into the ring and promoter Eddie Hearn confirmed Joshua?s next fight would be against the Ukrainian.
"You want a big fight and you've got it," said Klitschko to the crowd.
Joshua, the 2012 Olympic gold medallist, made a measured start against Molina and was content to take his time behind his jab in the first two rounds, before unleashing his power punches early in the third.
Molina, 34, looked comfortable for most of the first round, except for a ramrod jab that rocked him back on to his heels.
Joshua, 27, boxed cautiously in the second round as well, catching Molina at close range with a left uppercut but he did give the challenger anything to be concerned about until the third round.
Joshua unloaded with more venom in the third and then caught Molina flush with a right to the jaw in the American?s corner.
Molina only just beat the count and when the action resumed Joshua landed a quick flurry of punches which was enough for referee Steve Gray to call the fight off.
Molina lasted nine rounds with Deontay Wilder, who holds the WBC version of the world title, before his fellow American knocked him out last year.
But Joshua got the job done quicker and only two boxers have managed to take the north Londoner beyond three rounds.
Molina, who had only been drafted in as an opponent at less than six weeks? notice after Klitschko decided not to box Joshua, suffered his fourth career defeat in his 29th fight.
British heavyweights Dillian Whyte and Dereck Chisora settled their domestic dispute, which came close to being scrapped earlier in the week, with Whyte winning a controversial split points decision.
Whyte won by 115-114, 115-114 to 115-113 in an the eliminator for the WBC world heavyweight title, held by Wilder.
Briton Khalid Yafai lifted the vacant WBA world super-flyweight title unanimously on points after flooring Panama?s Luis Concepcion in the tenth round with a left hook.
Concepcion lost his WBA world super-flyweight title on the scales when he failed to make weight on Friday for a first defence against Yafai who earned scores of 120-108, 119-108 and 117-110.