Carlos Saucedo's brace, which came either side of Charles Aranguiz's first-half equaliser, saw Bolivia on track for a shock win.
But their winless run was extended to 14 matches and they stay without an away win since March 2007 after Vidal's controversial 91st-minute penalty in Antofagasta.
Substitute Pablo Hernandez went down under the slightest bit of contact from Edward Zenteno, who was shown his second yellow card.
Chile captain Claudio Bravo returned to Barcelona after Friday's win over Peru, while Gary Medel and Vidal took their spots in the starting XI despite injury worries.
It was a manic start to the encounter as neither team could settle in possession.
Unsurprisingly, Chile did so first and looked the more likely to open the scoring before Saucedo's 14th-minute goal.
Under pressure, Medel looked to play a back pass to Johnny Herrera – replacing Bravo in goal – only for Saucedo to intercept before neatly chipping the goalkeeper.
Alexis Sanchez went close to equalising moments later as his 20-yard free-kick took a deflection and went just wide.
Chile piled on the pressure and Aranguiz threatened, heading over a cross from the impressive Mauricio Isla.
Vargas curled a long-range effort over before the hosts got a deserved equaliser three minutes before half-time.
Aranguiz was on hand to take a touch inside his defender before passing the ball in after Bolivia keeper Romel Quinonez could only parry a tame Vargas volley.
Quinonez denied Chile the half-time lead with a strong left hand keeping out Sanchez's header from an Isla cross.
Sanchez had a shot cleared off the line early in the second half before Bolivia took the lead for a second time in the 51st minute.
Saucedo was given too much space and time on the edge of the area before firing into the corner.
Bolivia looked on track to hold on before the late penalty decision as Hernandez went down easily and Vidal put his spot-kick into the top corner.
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.