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The Pacific island side, hoping to make it to the last eight for the first time since 2007, were 9-0 down at the break after penalties by Georgia’s Luka Matvaka and Davit Niniashvili (2).
Fiji came alive in the second half with tries by Waisea Nayacalevu and Vinaya Habosi, converted by Frank Lomani, who also slotted a penalty before Matvaka added a late penalty for Georgia.
Fiji moved second in Pool C on 10 points, needing a point against Portugal in their final game to advance, while Georgia, who have three points, are eliminated and Australia, on six, look likely to be knocked out in the group phase for the first time.
Group leaders Wales have qualified for the quarterfinals.
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