Warren Gatland‘s men sit top of the table in the Pool of Death after what was their third win in as many games.
Being pushed all the way by a feisty Fijian outfit, Wales struggled for most of the game but tries from Gareth Davies and Scott Baldwin and 13 points from the perfect boot of Dan Biggar eventually secured the goods.
True to their style, Fiji’s running game forced Wales to scramble in defence a few times but it was at the set piece that they applied most pressure – something Gatland and his staff will be looking to address before taking on Australia next Saturday.
Vereniki Goneva was the try scorer for the Pacific Islanders while Ben Volavola kicked eight points from the tee.
“Fiji threw everything at us, it was a tough game,” said Wales coach Gatland.
“Our players showed a heck of a lot of courage there tonight and they dug deep, particularly with the five-day turnaround. We just needed to win and they hung in there… we’ve got a chance now.
“The boys will be at home tonight, Friday and Saturday off back with their families, and then come in on late on Sunday and travel up to London to prepare for the Australia game. They could do us a big favour but we’ll just have to wait and see.
“It’s nice to be in the position we’re in, a win today gives ourselves a chance and we’ll just see what happens at Twickenham.”
Davies, who scored the late crucial try against England on the weekend, picked up where he left off finding a gap to score under the posts and, after Biggar’s conversion, Wales had an early 7-0 lead.
But Fiji found their feet and they got back into the game using their set piece. A scrum penalty handed Volavola the opportunity to put his side on the board and the fly-half made the best of it with a sweet strike.
A lineout penalty gifted him with a second shot at goal but he was off target this time.
Davies was proving a handful in this first half and quickly tapping a penalty he put Fiji at sixes and sevens in defence.
A brilliant tackle from Volavola stopped him but the Islanders gave away a penalty and Biggar slotted it to extend their lead.
Just after the half hour, Wales got their second try of the game as Baldwin barged over after Tyler Morgan came close from scoring down the left flank.
Biggar was on target again and Wales led 17-3.
But another penalty at the scrum helped Fiji close the gap to 17-6 at the break as Volavola found his radar again from the tee.
The game opened up early in the second half and Fiji made it a four-point game as they scored one of the try of the tournament.
From his own 22, London Irish new winger Aseli Tikoirotuma opened up the Welsh defence and two offloads and 80 metres later, Leicester’s Goneva resisted two tacklers to score.
Volavola converted and Fiji were only trailing 17-13 with 30 minutes left on the clock.
Biggar gave Wales some room with his second penalty of the game but Fiji piled on the pressure and came close from scoring on two occasions.
Another defensive scrum saw Fiji put Wales on the back foot but from the turnover they conceded a penalty and Biggar opened a ten point lead with just over 10 minutes to go.
The hosts were in control now and they threw everything they had into securing the all-important try bonus-point.
They could not do so but they have one foot in the quarter-finals and remain in control of their destiny going into the last round of matches.
Wales: Matthew Morgan (Bristol); Alex Cuthbert (Cardiff Blues), Tyler Morgan (NG Dragons), Jamie Roberts (Harlequins), George North (Northampton); Dan Biggar (Ospreys), Gareth Davies (Scarlets); Gethin Jenkins (Cardiff Blues), Scott Baldwin (Ospreys), Tomas Francis (Exeter); Bradley Davies (Wasps), Alun Wyn Jones (Ospreys); Dan Lydiate (Ospreys), Sam Warburton (Capt., Cardiff Blues), Taulupe Faletau (NG Dragons).
Replacements: Ken Owens (Scarlets), Aaron Jarvis (Ospreys), Samson Lee (Scarlets), Luke Charteris (Racing 92), Justin Tipuric (Ospreys), Lloyd Williams (Cardiff Blues), Rhys Priestland (Bath), James Hook (Gloucester).
Fiji: Metuisela Talebula; Timoci Nagusa, Vereniki Goneva, Lepani Botia, Aseli Tikoirotuma; Ben Volavola, Nemia Kenatale; Campese Maafu, Sunia Koto, Manasa Saulo; Tevita Cavubati, Leone Nakarawa; Dominiko Waqaniburotu, Akapusi Qera, Netani Talei.
Replacements: Viliame Veikoso, Peni Ravia, Leeroy Atalifo, Nemia Soqeta, Malakai Ravulo, Henry Seniloli, Joshua Matavesi, Kini Murimurivalu.