Luis Suarez twice hit the post before Cavani netted from close range three minutes into the second half to give Oscar Tabarez's side a deserved victory.
Suarez saw his second-minute effort come back off the woodwork before another attempt by the Barcelona forward just after the half-hour mark also hit the post following an under-hit back pass by Wales defender Ashley Williams.
Cavani scored the only goal when a long ball out of defence set Cristian Rodriguez free behind the Wales backline and the winger cut his pass into the path of Cavani, who rolled the ball in from close range.
The Paris St Germain forward should have doubled the lead five minutes later from a similar position but mis-hit his shot.
At this year's World Cup, Uruguay will face Saudi Arabia and hosts Russia after kicking off their campaign against Egypt.
Earlier on Monday, there was further embarrassment for China who were thumped 4-1 by the Czech Republic after the tournament hosts were thrashed 6-0 by the Welsh on Friday.
(Reporting by Michael Church, Editing by Ken Ferris )
