Chile dominated a bruising contest, Eduardo Vargas and Arturo Vidal both going close before Edinson Cavani was sent-off for a second yellow card.
Uruguay held out until the 82nd minute when Isla smashed home from 16 yards. In the closing moments of an ugly game Uruguay defender Jorge Fucile was red carded for a second caution.
Chile will now face the winners of Friday’s match between Bolivia and Peru (00:30 BST) for a place in the final.
For Uruguay, their tournament ended in disgrace in a stormy game which saw six yellow cards in addition to two reds at Estadio Nacional in Santiago.
The biggest talking point before Isla’s winner was Cavani’s first red card for Uruguay on his 76th appearance for his country.
Yellow card
Having been shown a yellow card for confronting a linesman, the 28-year-old Paris St-Germain forward was ordered off after catching defender Gonzalo Jara off the ball.
Jara theatrically fell to the ground but Cavani, whose father was involved in a fatal car crash in Uruguay this week, could have few complaints.
He argued with the referee for several minutes before finally being persuaded to leave the pitch.
Uruguay self-destructed after falling behind, Fucile sent off for a second booking with two minutes remaining after bringing down Alexis Sanchez.
The match was then halted for several minutes after Uruguay’s players surrounded the referee and linesman and officials and players from both sides scuffled on the field.
Chile, who dominated the match with 80% possession, have never won the Copa America since its inception in 1916.
The other two quarter-finals feature Argentina against Colombia (00:30 BST) on Saturday and Brazil versus Paraguay on Sunday (00:30 BST).
Credit: BBC
