The 30-year-old Newcastle forward was playing his eighth Test for Fiji, but it was his first game back after being banned for four matches for a dangerous tackle in the round-26 NRL game against the Warriors, which wiped out his finals campaign for the Knights.
In the 28th minute, he followed a Brandon Wakeham kick towards the posts and ripped the ball out of Cook Islands fullback Esom Ioka's grasp to plant the ball under the black dot at McDonald Jones Stadium on Sunday afternoon.
Saifiti was also making a welcome return to the Bati jersey, playing his last games during the 2017 World Cup.
"He's a great acquisition to our team, so to have him back after being away for a long time is fantastic for Fiji rugby league," coach Mick Potter said.
It was one of five first-half tries by the Bati, who were in a dominant mood and took a 28-0 lead into the sheds.
The Cook Islanders scored two fine tries in the second half, but the Fijians scored more points including a double by centre Solomon Saukuru.
"It seems to be a trait by us. For the last four years I've been involved with this team it takes a while for us to start clicking," said coach Karmichael Hunt.
"I'm glad we ended up finding some footy, but we were our own worst enemy in the first half."
Fiji were expertly led by skipper Api Koroisau with his defence and attacking kicks, and then there was the creativity of halves Kurt Donoghoe and Brandon Wakeham, who had five line-break assists and five try assists between them.
A measure of the Cook Islanders' frustration was Hunt pulling halfback Esan Marsters from the field in the 55th minute, replacing him with 14-Test veteran and former captain Brad Takairangi.
The coach later said Marsters had been troubled by an Achilles tendon coming into camp.
"So it was really more about getting some fresh legs on there, but maintaining some experience with Taks," Hunt explained.
Four minutes later and they were on the board after a show-and-go by five-eighth Maui Winitana-Patelesio. Proving that was no fluke, prop Davvy Moale barged over four minutes later, making the scoreline a little more palatable at 34-12.
Things don' get any easier for the Cook Islands as they now face New Zealand in Christchurch next Sunday, while the Bati are also taking on another World Cup heavyweight in defending champions Australia at Suncorp Stadium a day earlier.
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