With Fiji leading 13-7, wing Eroni Sau was sent off for a reckless swinging arm on Johnny Williams in the 25th minute.
The visitors also picked up two yellow cards.
Hooker Ryan Elias scored twice with Kieran Hardy, Alex Cuthbert, Louis Rees-Zammit and Liam Williams also scoring as Wales finished strongly.
Wales host Australia next Saturday to end their autumn series, having lost to New Zealand and South Africa before overcoming Fiji.