With the first leg having finished 1-1 in Mexico, Escobar's four-minute double in the dying stages saw The Strongest progress.
Nestor Craviotto's men take their place in Group Four, alongside Emelec, Internacional and Universidad de Chile.
The away goal scored by The Strongest appeared to be set to be enough to send them through.
Tuesday's clash in a very wet La Paz was locked at 0-0 entering the final 10 minutes, with the visitors needing a goal.
Instead, Escobar put the hosts ahead in the 86th minute - curling a left-footed effort into the bottom corner from just outside the area after Alejandro Chumacero's lay off.
Just three minutes later and Escobar sealed the tie by driving into the area and finding the bottom corner once more.
In Argentina, hosts Huracan and Alianza Lima played out a 0-0 draw - that seeing the former claim a 4-0 aggregate win.
Huracan will be in Group Three, taking on Cruzeiro, Mineros de Guayana and Club Universitario.
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.