The flying 22-year-old scored the first hat-trick of his NRL career, producing a sensational diving finish for one try and displaying fantastic hands for another at Bankwest Stadium.
Canterbury threatened to pull off a comeback at the death after Christian Crichton scored an intercept try, but Cronulla scrambled desperately to secure their second win of 2020.
Sharks coach John Morris shook his head in disbelief at Katoa's brilliance post-match.
"He's just such a great kid, Sione. He's worked so hard on his game," Morris said.
"I see that at training all the time, he's got beautiful hands. It just comes natural to him.
"In wet and greasy conditions, to pick that up off his bootlaces like that [for his second try], it was a real big play for us."
Sharks halves Chad Townsend and Shaun Johnson combined well, recording two try assists apiece. Townsend hadn't registered a try assist this season beforehand.
Morris said he was never worried about the No.7's form.
"[Townsend] does so much in and around our team off the ball, setting up our shapes," Morris said.
"He's also got one of the most skilful back-rowers in the game playing outside him, and a lot of our attack does come off Wade Graham."
Matt Moylan started at fullback for Cronulla in his return from a hamstring complaint but switched with Josh Dugan to defend at left centre midway through the second half while roving in attack.
Moylan was forced from the field for a HIA with 18 minutes remaining after being crunched by Dallin Watene-Zelezniak. He passed the test and returned for the closing stages.
"It's important to note, that was only the fourth or fifth time that [Moylan] has played with Wade, Shaun and Chad over the last 18 months," Morris said.
"That's quite bizarre. So it's really good for me that he's pulled up okay and he sort of had a bit of a hybrid role ... That was just a way of easing him into it."