Reds winger Vunivalu was shown two yellow cards - both for foot-tripping - resulting in a red card early in the second half which left the visitors one man down for much of the second half in heat-sapping conditions.
Reds captain Liam Wright rued his team's slow start.
"We got punched in the face a bit, early. Our contact wasn't good enough, we fell off tackles and Fiji ran hard, especially in front of their home crowd," he said.
"We found a way back into that game, but ill-discipline killed a lot of the opportunities we were creating."
The eighth-placed Drua scored three tries to two in notching a fifth win from six home matches this season and took a major stride towards reaching the playoffs for a second straight season.
Drua captain Tevita Ikanivere crossed twice while the home side were also awarded an early penalty try, conceded by Vunivalu when he tripped Kitione Salawa as the Drua flanker closed on the try-line.
Hooker Ikanivere scored soon afterwards, but the Suva crowd was silenced when Reds winger Floyd Aubrey and fly-half Lawson Creighton responded with tries for the Reds as they trimmed Drua's lead to 15-14 at halftime.
The home side -- who were particularly adept at turning over Reds ruck ball -- stayed in front throughout the second half, aided by Vunivalu's trip on opposite number Selestino Ravutaumada during an attack.
The Reds remain fifth in the table, but defeat in Suva dented their hopes of a top-four finish and a home quarter-final with two rounds remaining in the regular season.
The Drua hope to snap their winless record on the road this season when they face the Highlanders in Dunedin next weekend.
