Warren Gatland said Wales had to call on all their reserves to beat Fiji 23-13 in Cardiff and stay on course for a World Cup quarter-final place.
Although Wales missed out on a try bonus point, they top Group A and will be through if England fail to beat Australia at Twickenham on Saturday.
First-half tries from Gareth Davies and Scott Baldwin put Wales ahead but Fiji came back strongly after the break.
"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."
With scrum-half Davies squirting over from close range and hooker Baldwin crashing over, Wales led 17-6 at half-time at the Millennium Stadium and looking good to add the two more tries necessary to claim a bonus point.
But the efforts of beating England five days before at Twickenham seemed to take its toll on the Wales players in the second half, as Fiji ran hard and scored a deserved try through Niki Goneva.
"That was so tough," admitted Wales captain Sam Warburton. "The first half, I was knackered.
"Our priority going into the game was to win. It was a really quick game and very tough for us but we've got three wins out of three.
"If somebody had told us that at the start of the campaign we'd bite your hand off."
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Wales now have a welcome rest before facing Australia on 10 October in their final pool game, although the pressure could be off if the Wallabies beat England on Saturday to put the hosts out of the tournament.
"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," Gatland added.
"Australia 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."