The Highlanders’ Dutch-born lock Fabian Holland, who qualifies to play for the All Blacks next season, came on in the second half.
Other notables playing for the Barbarians included the former French midfielders Gael Fickou and Virimi Vakatawa and the Japan-based Jack Cornelson, son of Greg who scored four tries against the All Blacks in a Bledisloe Cup test at Eden Park in 1978.
Epeli Momo, who plays for the Fijian Drua in Super Rugby Pacific, scored a hat-trick for Fiji.
The Barbarians-Fiji match followed the Wales-Springbok test at Twickenham and was played before more than 65,000 spectators.
The Springboks won 41-13.
Burke, the son of Richard and Julie Burke, missed most of the Crusaders’ disastrous season - ninth out of the 12 teams - because of a ruptured Achilles tendon suffered playing for Canterbury last year.
He will play for Canterbury in this season’s NPC before taking up his Saracens contract.
Following his primary and intermediate schooling in Gisborne, Burke attended St Paul’s Collegiate in Hamilton,
He represented the New Zealand Barbarians Schools’ team in 2017.