Bayern Munich midfielder Vidal rose highest after Alexis Sanchez's cross and left goalkeeper Fabrice Ondoa no chance with a strong header in the 81st minute before Vargas put the result beyond doubt well into stoppage time.
Vargas previously felt he was unfairly denied a goal late in the first half, with the 27-year-old already celebrating, only to then be deemed to be in an offside position after VAR referral, even if replays of the goal did not provide any clarity as to whether he indeed found himself in an illegal position.
But VAR referral did see him add his name to the scoresheet in the 91st minute, with referee Damir Skomina initially disallowing the goal for offside, only to eventually award the strike after conferring with his assistant.
Juan Antonio Pizzi had opted to bench Sanchez for Sunday's encounter as the Arsenal man continues his recovery from an ankle injury, but the attacker played a key role in his side's win in the end as he had a hand in both goals.
The Chileans now meet Germany on Thursday in their second Group B game, while Cameroon face the Caltex Socceroos on matchday two.