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Marc Sneyd's drop-goal had put Hull 29-28 up in the 77th minute, but the imposing Folau expertly leapt to field James Maloney's subsequent short kick-off with a one-handed catch.
From there Catalans advanced towards their hosts' line and Maloney scored to seal a remarkable win which saw Steve McNamara's men overturn Hull's 18-point lead with a stirring second-half display.
McNamara, Catalans' Hull-born coach, said: "I thought Izzy was solid without being spectacular.
"But to come up with a short kick-off and for Izzy to take it one-handed, and give us a last chance to win the game, we are obviously pleased how it has ended.
"It was a special play and a special catch, but I thought we under-used him.
"If we use him better, his influence will grow throughout the season, without a doubt, because he has the talent.
"But we never got him into any space today. We never got the chance to see him run and we never kicked the ball to him.
"Yet he worked hard for the team and that's the fundamental thing - then all the other bits come into play."
Much of the pre-match talk had centred on Folau being targeted with protests against his views.
There was a handful of rainbow flags waved before kick-off and a smattering of boos greeted his first touch, but he was hardly entering a lion's den.
McNamara added: "We wanted to make it a graveyard because if Hull get on top, the crowd get up for it and it's an incredible place to be a Hull player.
"But if you can turn the screw on them, you can make it very quiet and we certainly did that by the end."
Folau won 73 caps for the Wallabies and scored 37 tries, including a brace against England at Twickenham in his final appearance for them in November 2018.
After his rugby union career ended last year, he was barred from returning to rugby league in the NRL.
Nevertheless, Folau was handed a lifeline by Catalans and has remained in excellent physical condition.
His first touch was jeered and he conceded a penalty which led to an opening try for Hull's Mahe Fonua.
Benjamin Jullien and Fouad Yaha replied for Catalans but Fonua's second and Carlos Tuimavave's try put Hull 16-10 up at the break.
Further scores from Jamie Shaul and Manu Ma'u appeared to have put them out of sight at 28-10.
Yet the outstanding Sam Tomkins was instrumental in a fightback which harvested three quickfire scores for Jullien, Josh Drinkwater and Samisoni Langi, levelling matters at 28-28.
After Sneyd's one-pointer put Hull back in front, there was still time for that late intervention from Folau, who stands almost 6ft 4in, which produced the winning score.
Hull coach Lee Radford, whose supporters paid tribute to former player Adam Maher following his recent passing from motor neurone disease, said: "You can try and guard against that, but unfortunately we don't have anyone in our team who can jump that high."