The scorecards were in wide favor of Joshua, 118-110 twice and 119-109.
Victory extended the London 2012 Olympic champion' flawless professional record to 21 wins from as many bouts but all of his previous successes had been by way of knockouts.
Joshua, 28, beat Parker, 26, on points last night to secure the WBA, IBF and WBO belts.
Parker was escorted by Samoan chiefs as he arrived for the biggest battle of a 24-fight career, followed by the home favourite Joshua, whose white robe was lit up by pyrotechnics while he strolled confidently towards his 21st opponent. Immediately after Parker landed a left hook but it was Joshua's round. I think it's a fight Anthony Joshua wants and I think he really wants it this year.
Many viewers have complained that the bout was spoiled by the referee and Parker's team were not happy with him from the get-go, as they claimed that the Italian referee couldn't speak English.
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Joshua said he did not condone comments Wilder is now under investigation by the WBC for after he stated he wants "a body" on his fight record.
Perhaps the biggest threat lies outside the heavyweight division in Oleksandr Usyk (14-0, 11 KOs), the Ukrainian who holds two cruiserweight world titles and faces Murat Gassiev for the other two on May 11. "Absolutely robbed! 12 rounds Parker!"
"Today I got beaten by a better champion".
"This was about boxing finesse - I stuck to my word".
Tyson Fury reacts to the Anthony Joshua and Joseph Parker fight...
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"2018 was always a time to capture all the belts", said Joshua, flanked by promoter Eddie Hearn and trainer Rob McCracken.
"Of course, I'm young, fit and strong. I thought it was hard, but going the 12 rounds was light work".
"Look at every one of these belts now, I will have to be the most powerful man on a negotiating table". Although those backing Joshua outnumbered Parker's support, he received a healthy portion of cheers from the crowd.
Joshua began to measure Parker with his own ramrod jab in the second, while the Kiwi was muscled to the ropes by a crunching combination in the third.
But Parker made some good connections in the fifth and there was a furious exchange early in the sixth, before Quartarone intervened. Joshua has three options for his next opponent. This was the first time Joshua relied more on his boxing IQ than his predatory approach, to get the job done.
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X-rays on McKinney and Warren both came back negative, though Boone suggested McKinney could miss "at least a few weeks". I'll tell myself it can't get any worse than this and overcome my issues before my next start". "I can't do that".