Warren Gatland’s side scored four tries as they held on amid a dramatic conclusion with the Fijians threatening to snatch victory.
After looking out of sight following tries from Josh Adams, George North, Louis Rees-Zammit and Elliot Dee, Wales almost blew a 32-14 lead late on.
Late scores from Josua Tuisova and Mesake Doge left Welsh fans on the edge before Semi Radradra dropped the ball in the last play of the game to wrap up the contest for Wales.
The wonderful eight-try spectacle evoked memories of when Fiji defeated Wales 38-34 in Nantes in 2007, but this time the men in red were the ones celebrating at the end with fly-half Dan Biggar named man of the match after kicking 12 points.
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