Luai had three try assists and Kai Pearce-Paul scored twice on club debut, with the Tigers racing to a 28-2 half-time lead and never looking back.
The long-time strugglers' hopes of breaking their notorious 14-year finals drought won't be decided by a big win at sold-out Leichhardt Oval in March.
But Benji Marshall couldn't have asked for much more following the Tigers' round-one bye, as expectations lift for his third season at the helm.
"It's exciting, but at the same time I think it's just about being humble," Luai said after the superb start to the season.
"It's only round two. We've got a lot of work to do."
Right centre Taylan May injured his right shoulder in the first half and was replaced by Jeral Skelton in the only sour note for the Tigers.
"He seemed OK, but the medical staff said it's not worth the risk to put him back on, so he'll get scanned," Marshall said.
The win eclipsed a 16-point win over South Sydney in 2017 and became the Tigers' most one-sided victory to begin a season in 27 years as a joint venture.
The Cowboys underwhelmed during their own first clash for 2026 in Las Vegas, and a heftier loss on Saturday keeps pressure on coach Todd Payten.
"I thought we started physically, but then it just snowballed very, very quickly," Payten said.
The visitors gave up five set restarts in the opening 10 minutes, then leaked two tries while Kai O'Donnell was in the sin bin for repeated infringements.
"We're going to seek some clarification," Payten said.
"Kai was sent to the bin, but he actually didn't affect a tackle, so I was a bit confused.Â
"Another ruck infringement would have sufficed (rather than an off-side penalty)."
The Cowboys were on the back foot from the sin-binning, though briefly threatened to make a game of things with two tries in five minutes midway through the second half.
Api Koroisau gave O'Donnell a cheeky wave as he left to the sin bin, and moments later Luai passed inside and put Samuela Fainu over on the left.
Second-rower Pearce-Paul grabbed a beautiful short ball from Jahream Bula to score his first try since joining from Newcastle, before pouncing on a Luai grubber kick for his second.
Perth-bound Luke Laulilii put the cherry on top of a great half by crossing from a scrum play a minute before the hooter.
Superb in the first half, five-eighth Luai had his own try in the second by regathering his grubber kick after it hit the upright.
Laulilii put paid to any hopes of a Cowboys comeback by picking off a Scott Drinkwater pass and sprinting 70 metres to confirm his double.
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