In Monday's match, Cavani struck nine minutes from the end of a dour contest at the Maracana stadium in which both teams managed only three shots on target, reports Xinhua news agency.
Chile opened brightly with Alexis Sanchez sending a shot over the crossbar and Charles Aranguiz seeing his long-range effort palmed away by Fernando Muslera.
But Uruguay grew in confidence and Giorgian Di Arrascaeta had his team's first chance after receiving a Luis Suarez pass and then thumping an attempt from 25 yards into the stands.
Then it was Suarez's turn to miss an opportunity as he rounded Gabriel Arias, only to see the goalkeeper recover to turn the Barcelona forward's shot behind for a corner.
Uruguay continued to press and Martin Caceres did well to make clean contact with his weaker right foot, sending a volley just wide of the target.
The second half continued in the same vein as the first, with both teams lacking creativity in the final third.
Diego Godin's tame header from a corner was easily saved by Arias, while at the other end, Sanchez blasted over the bar from distance.
Uruguay had Jose Gimenez to thank in the 70th minute, after Muslera came off his line at a corner and the ball fell to Marcelo Diaz, whose goal-bound header was cleared off the line by the Atletico Madrid defender.
Chilean fans accounted for most of the 57,000 spectators and they were sent into stunned silence when Cavani struck with nine minutes remaining.
The 32-year-old latched onto Javier Rodriguez's cross with a superb glancing header that left Arias with no chance.
The result means Uruguay will meet Peru in the quarterfinals at Salvador's Fonte Nova Arena on June 29. Chile, who finished second in the group, face Colombia at Sao Paulo's Corinth Arena the previous day.
( With inputs from IANS )