Isla's low drive from the edge of the area was enough for the hosts to progress following an ill-tempered match that saw Edinson Cavani and Jorge Fucile sent off in the second half.
There will certainly be questions asked about the level of officiating, with Brazilian referee Sandro Ricci having a poor night.
Cavani was the first to see red, given his marching orders in the 63rd minute after picking up a second yellow card. The Paris St-Germain man had endured a tough build-up to the match, with his father arrested for allegedly causing a fatality while driving under the influence of alcohol, and it showed, with the striker shown his first yellow following an altercation with one of the linesmen before seeing red after appearing to slap Chile's Gonzalo Jara.
Uruguay looked solid defensively throughout, but they were undone with less than 10 minutes to play, with Isla capitalising after a poor punch from Fernando Musclera. A looping ball was played into the area from the left and Musclera came out to punch, but his clearance only went as far as the edge of the area where it was controlled and nudged to Isla who found the bottom corner of the net with a driving effort.
Any chance Uruguay may have had of snatching a late equaliser where all but extinguished in the 88th minute when Fuclie was sent off after a poor challenge on Alexis Sanchez. The game was held up for a number of minutes after the players engaged in pushing and shoving following the incident, with the Uruguayan players not shy to express their anger and frustration towards Ricci.
Once play was resumed Chile were able to see out the remaining minutes to book a place in the last four as they go in search of their first Copa America title.
Uruguay adopted a physical approach to the match, but despite trying to bully their hosts it was Chile who had the better of the first half.
Sanchez, Arturo Vidal and Jorge Valdivia all had chances to open the scoring in the opening 45 minutes, but were unable to find the back of the net. It was Aranguiz who had the best of the opportunities, but he failed to make the most of the chance afforded to him and fired his effort straight at Musclera.
Vidal came close with a bending effort after the break, before Diego Rolan nearly grabbed a goal against the run of play in the 53rd, but his effort was straight at Chile keeper Claudio Bravo.
Despite going a man down, Uruguay engineered two good opportunities, but could not break the deadlock.
It was left to Isla to grab the decisive goal, with the full-back's low effort getting the job done before the match deteriorated in the closing stages.