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.
"We'll take a win but we are disappointed with our performance. We lacked basic skills and lost the ball too often," stand-in Wales captain Gethin Jenkins told the BBC.
"But all credit to Fiji, they came here and gave us a hell of a game. I'm just glad we got on the right side of the scoreboard. We weren't at the races but at least we got the win."
Liam Williams, deputising for concussed British and Irish Lions fullback Leigh Halfpenny, was the rare bright spark in what was a laboured Welsh performance.
He was joined in the starting line-up by experienced playmakers Mike Phillips and Rhys Priestland but they struggled to establish any structure or cohesion in a match littered with basic errors.
Following Ma'afu's dismissal, Wales had 27 minutes with an extra man but were utterly wasteful and were made to sweat after Nadolo converted his own try to take his personal tally to 13 points.
Fiji had 60 seconds to register the most improbable victory but Wales survived the late scare in a game which had shades of their 38-34 defeat at the hands of Fiji which knocked them out of the 2007 World Cup.
