Uruguay were reduced to nine men by the end of the game with Edinson Cavani sent off for a second yellow card after 62 minutes and Jorge Fucile also shown red for a second booking with two minutes remaining.
After Fucile's exit, the match was halted for several minutes as Uruguay's players surrounded the referee and officials and players from both sides scuffled on the field. The holders looked hard done by after video evidence showed it was Gonzalo Jara who first gave Cavani a friendly slap and then poked him behind the referee's back.
When Cavani touched Jara's face with the slightest of taps, he fell to the ground to provoke a second yellow for the Paris Saint Germain striker.
"There's a bitter taste in our mouths," Uruguay manager Oscar Tabarez told reporters. "I've seen the television and photographs, that's where the truth is."
Mauricio Isla scored the only goal in the 82nd minute when he fired home from 15 yards after Uruguayan goalkeeper Fernando Muslera had weakly punched away a cross. Hosts Chile, who dominated the match with 80 percent of possession, have never won the Copa America since its inception in 1916 and now face the winner of Thursday's Peru-Bolivia tie.
"We now have another game I don't know if it will be Peru or Bolivia but we still have the dream," said striker Alexis Sanchez.
"We fought hard and we have to thank the fans who were behind us all the way." In the other quarter-finals, Argentina face Colombia on Friday and Brazil play Paraguay on Saturday.
(Writing by Andrew Downie; Editing by Greg Stutchbury)
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