Chile, reigning two-time Copa America winners, were without Arsenal star forward Alexis Sanchez to begin the match but he came on as a second-half substitute later on.
Chile coach Juan Antonio Pizzi had said the Gunners forward was a doubt after hurting his left ankle in training on Thursday, and confirmed that worry when he released the team sheet and Sanchez was not included in the starting XI.
Chile enjoyed the lion's share of the possession in the first half, with Vargas hitting the post in the first minute to signal their attacking intent, though Cameroon maintained a threat on the counter-attack
However, clear chances were hard to come by until Vargas fired high and well over the bar after being played into a pocket of space in the 40th minute by Vidal.
Chile had a goal disallowed just before half-time. Getty
Chile looked to have found their breakthrough just before the stroke of half-time -- Vidal again feeding Vargas in behind the defence for the forward to fire home -- but the Video Assistant Referee system adjudged the Tigres man to be offsides despite appearing to be in a legal position.
Cameroon showed more initiative after the break, keeping possession and creating danger for the Chilean defence.
Sanchez came on in the 58th minute for Edson Puch in attempt to inject more thrust to La Roja's attack.
And the Arsenal man made a difference in the 81st minute, when his cross found Vidal free in the box for the Bayern Munich man to head down and past Joseph Ondoa in the Cameroon goal.
Vargas finally secured his goal in the 90th minute when he fired home after Sanchez rounded the keeper and saw his shot saved by a defender. The goal was initially ruled offsides by the replay system later awarded him the goal after deliberation.