After a dispiriting build-up to the tournament marred by injuries to key players, the Welsh moved level with England at the top of Pool A on five points ahead of the teams' seismic clash at Twickenham next Saturday.
"It was a very tough game, Uruguay made it tough for us right from the start," Wales coach Warren Gatland told reporters.
"It was quite dewy out there and the ball was a bit slippery so there were a few turnovers but we're satisfied to get the first one under our belt and to get the win."
Wales, fielding several second-string players, made a sluggish start, conceding a succession of turnovers, and Uruguay flyhalf Felipe Berchesi kicked two penalties to put his largely amateur side 6-0 ahead.
The hosts, however, responded swiftly, much to the delight of a raucous and excitable crowd at the Millennium Stadium.
Prop Samson Lee grounded the ball over the line following a ferocious driving maul and Allen ran on to a neat chip through by Rhys Priestland to score the second try.
Man-of-the-match Allen scampered over again and completed his hat-trick after a flowing Welsh move down the left to take the hosts 28-9 ahead at halftime.
Gatland made a number of replacements with the tougher group matches against England and Australia in mind, but his team continued to cut through the Uruguayan defence almost at will.
Winger Hallam Amos surged over the line before the crowd's celebrations were briefly dampened when Allen left the field with a hamstring injury, the third Wales player forced off.
Scrumhalf Gareth Davies grabbed the sixth try with a sniping run as Uruguay, ranked 19th in the world and playing in their third World Cup, worked tirelessly to keep the scoreline respectable.
"I'm still proud of my players after the performance," Uruguay coach Pablo Lemoine told reporters.
"We are not worried about the result, that was normal for the level and the feeling is positive.
"It was our first game at the Millennium Stadium against Wales and the first match against a tier one nation in some 15 years."
Flanker Justin Tipuric touched down after another powerful Wales maul and Davies crashed over for his second try in the final minute to complete a satisfactory start for Gatland.
Priestland slotted over seven of the eight conversions in the absence of regular kicker Leigh Halfpenny who misses the tournament due to injury.
Allen has torn his hamstring, props Paul James and Lee suffered calf strains and fullback Liam Williams was also forced off with a knock, leaving Gatland with plenty to ponder and his physios with a busy week ahead.
(Editing by Mitch Phillips)
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