Any suggestions this should not have been the main bill were put to bed with both fighters producing a masterclass in London.
Judge Benoit Roussel scored the fight 114-114, but Matteo Montella (117-112) and Alfredo Polanco (115-113) gave it to Taylor, much to the delight of the Scots and neutrals inside the O2 Arena who were behind the Tartan Tornado from the off.
The Edinburgh fighter now holds the WBC, WBA and IBF titles, the Ring Magazine belt and World Boxing Super Series Ali Trophy.
Taylor told Sky Sports: "What a fight, Regis is a great champion, but the best man won.
"He was very good, very strong and had good timing, but I knew I could get to him inside. He lived up to his name and he is a great fighter.
"I knew I could beat him with the jab alone, but he had me himself so respect to him."
In tartan shorts, Taylor overcame a swollen right eye and a cut above it late on to come through on a majority decision.
His strong jab troubled Prograis throughout and although the New Orleans boxer gave as good as he got, the Scot had too much in the end, landing big blows in rounds six and seven.
While Taylor's record now reads 16 fights, 16 wins, the American no longer has a zero in the loss column with this his first defeat in 25 bouts.
Prograis added: "The better man won on the night. No excuses, but I will be back. I am pretty sure Josh enjoyed it, hopefully we can do part two."
Derek Chisora delighted the home crowd earlier in the evening with a fourth-round victory over David Price to win the WBO Inter-Continental heavyweight belt.
Fighting on the undercard of the Taylor-Prograis fight, Finchley resident Chisora dominated from the first bell and almost finished the Liverpudlian at the end of the third.
Price was saved by the bell, but he was dropped in the fourth by a body shot and his corner made the decision to throw in the towel not long after.
Chisora, 35, told Sky Sports: "I am an old boy in this game. I came to destroy. I knew if I caught him, he was gone."
Merseyside fighter Price struggled to land blows on his opponent and in the third the bout almost came to an end.
The Olympic bronze medallist was caught by several combinations and, despite a brief response, it was the bell at the end of the third which saved him.
A chat with his corner was not enough time for the heavyweight veteran to regroup and he dropped to the canvas after a body shot midway through the fourth.
Despite attempting to continue, his team had seen enough and Chisora could celebrate the 32nd win of his career.
He paid tribute to his rival and close friend afterwards, adding: "David Price stepped up to save the show so shout out to David Price, his family and his team."
Joseph Parker was Chisora's original scheduled opponent before the New Zealander pulled out due to illness.
"If we can get Joseph Parker as soon as possible – I hope he doesn't get a spider bite – let's do it as soon as possible," Chisora added.
But Chisora's manager David Haye added: "I like the Oleksandr Usyk fight. That would be a fantastic fight."
A few hours before Taylor's fight, fellow Scot Ricky Burns had lost out to Lee Selby in a majority decision after a close lightweight content.
The Welshman started strongly, but Burns defied his 36-year-old legs to come back into the bout, which saw both men trade blows after the bell had gone at the end of the fifth.
In the end, former IBF featherweight world champion Selby edged out his old sparing partner with the three judges scoring it 115-115, 116-112 and 116-113.
Also in London, Lawrence Okolie stopped Yves Ngabu in the seventh round to win the European cruiserweight title and add it to his Commonwealth and British belts.
Conor Benn, the son of Nigel, also defended his WBA Continental welterweight title with a fourth-round stoppage of Steve Jamoye.