Kiss will take over as Wallabies coach from Joe Schmidt after the July internationals, and eyebrows were raised when the Reds lost their season-opener to the NSW Waratahs in Sydney.
Successive wins over the Otago Highlanders, ACT Brumbies, Waratahs and Drua, however, have the Reds two points from the top of the standings in fourth place with 10 rounds of the regular season remaining.
Saturday's victory over the Drua - a first for the Reds in Fiji - was all the more impressive for the fact that the table-topping Wellington Hurricanes and third-placed Brumbies have been beaten in the stifling Fijian heat this season.
"It was significant for us today," Kiss told reporters after the 21-6 win.
"The huge respect we had for the Drua was represented by the way that we approached our defence.
"To keep them try-less I think was an unbelievable effort by the boys."
Kiss rested Wallabies Carter Gordon, Fraser McReight and Zane Nonggorr for the trip to Fiji but was rewarded with some fine performances from other players, most notably backup flyhalf Harry McLaughlin-Phillips.
Powerful Fiji-born winger Filipo Daugunu was immense on both sides of the ball, further strengthening his case for a starting role for the Wallabies in the July tests.
Kiss said there was still plenty of room for improvement for the team, especially with a trip to the New Zealand capital to face the red-hot Hurricanes coming up next weekend.
"We're making sure that we continue to grow our game," he added.
"There's elements of our game we're still not completely happy with, but when it matters the right things are happening for us. It's a credit to the boys, they just keep challenging themselves to be better at things.
"We weren't perfect but we found the right solutions at the right time today."