Setif dumped title-holders Wydad Casablanca of Morocco out of the elite African club competition by forcing a 0-0 second-leg draw in Casablanca to win 1-0 on aggregate.
Zeghba made a string of superb saves at the Stade Mohammed V to defy Wydad, for whom Liberian striker William Jebor was particularly wasteful.
Cabaca saved two penalties within four minutes as Primeiro came from behind to draw 1-1 with TP Mazembe of the Democratic Republic of Congo in Lubumbashi and advance on away goals.
The first match between the clubs ended 0-0 last weekend, leaving five-time champions Mazembe hot favourites to reach the last four.
Esperance scored late through Ivory Coast-born Fousseny Coulibaly to edge home side Etoile Sahel 1-0 in an all-Tunisia showdown in Sousse and qualify 3-1 on aggregate.
The remaining quarter-final is set for Cairo Saturday with record eight-time champions Al Ahly of Egypt and Horoya of Guinea level after a goalless first leg.
Primeiro face Esperance and Ahly or Horoya meet Setif in the semi-finals, scheduled for October 2 and 23.
The unexpected qualification of twice African champions Setif was masterminded by a former Wydad coach, Moroccan Rachid Taoussi.
After a disastrous start to the group phase, Setif have gone six matches unbeaten and they will now dream of emulating the 1988 and 2014 trophy-winning sides.
Defeat dashed Wydad hopes of becoming only the fourth club in 54 years after Ahly, Mazembe and Enyimba of Nigeria to become back-to-back African champions.
Cabaca used his right foot to block a Ben Malango penalty on the stroke of half-time and both hands to push away a Tresor Mputu spot-kick three minutes into the second half.
Mazembe also had two goals disallowed and struck the woodwork against Primeiro, who were appearing in the knockout stage for the first time.
Jackson Muleka got Mazembe off to a great start, rifling a close-ranges shot into the net on 12 minutes only for DR Congo-born Mongo Bokamba to equalise from a 34th-minute free-kick.
Coulibaly delivered the killer blow for Esperance three minutes from time after a dogged duel in a Mediterranean resort.
Scoring opportunities were scarce in a cagey clash between the arch domestic and African rivals and it always seemed that one goal would decide who advanced.