Vargas’s first-half strike saw him draw level with Peru’s Paolo Guerrero on 14 goals in the Copa America’s all-time goalscoring rankings, three behind the record of 17 held by Brazil‘s Zizinho and Argentina‘s Norberto Mendez.
The result left Chile with five points from three games and assures them of a place in the knockout stage.
Uruguay remain in fourth place with one point from two games following their opening defeat to Argentina.
The build-up to the game had been overshadowed by controversy in the Chile camp after revelations the team had breached COVID-19 protocols by bringing a local hairdresser into the team hotel.
However there was no sign of the controversy affecting their play, with Vargas firing Chile ahead on 26 minutes from a tight angle after latching onto a clever pass from English-born Ben Brereton.
Uruguay grabbed a share of the points in the second-half when Suarez bundled in the ball from close range during a tangle with former Barcelona team-mate Arturo Vidal at the far post following a corner.
Manchester United striker Edinson Cavani almost snatched victory for Uruguay in the 85th minute, but his glancing header flashed just wide of the post.