In an open first half, Wales scored unconverted tries through giant wingers George North and Alex Cuthbert and a converted penalty try following a collapsed maul to take a 17-6 lead into the break.
Fiji, whose response came courtesy of two Nemani Nadolo penalties, provided a number of dangerous moments through their typically expansive attacking rugby but were let down by a lack of composure and poor decision making.
Fiji prop Campese Ma'afu was shown a yellow card in the 36th minute for a series of infringements and within six minutes of returning to the field was shown a second yellow card for a dangerous tug on Bradley Davies.
Despite their numerical advantage, Wales struggled to break down Fiji who defended with a steely resoluteness which was non-existent in the first half.
After Toby Faletau had a late try ruled out, Nadolo intercepted a stray pass to race 70 metres to score.