Vunivalu previously played professional rugby league for the Melbourne Storm in the NRL, and Fiji at international level.

Melbourne finished as Minor Premiers in the 2019 NRL season and were favourites to win the premiership but were defeated in the preliminary final against the Sydney Roosters.

In December 2019 it was confirmed by the Queensland Reds that Vunivalu signed with the rugby union team, returning to the sport for the first time since he was eighteen-years old.

Early in the 2017 NRL season, Suliasi was selected for his Fiji Bati international debut at the Pacific Rugby League Test against Tonga, played at the Campbelltown Stadium in Sydney on 6 May.

On 10 November, he scored his second hat trick of tries in the 60th minute mark after beating Italy in the 38-10 win at Canberra Stadium.

After the Bati reached the semi-final, he was nominated for the Rugby League World Golden Boot Award, which was won by Storm teammate Cameron Smith.

[24][25] Coach Dave Rennie stated, after speculation of Vunivalu's place in the Wallabies squad for the Tri Nations Series, that "there’s no plan to use Suli in the two Argentina games unless we have got a spate of injuries," adding, "the key for him is to earn the right to play and [we are] keen to reward the guys who have been working for the last three months.

That same year, as part of the 2022 end-of-year rugby union internationals, Vunivalu debuted for the second national team, Australia A, against Japan.