After France-based Eneme converted, Malian Falaye Sacko had a kick saved by Jesus Owono and his country bowed out in the first knockout stage for the second successive Cup of Nations.
An ultra-cagey last-16 match produced minimal excitement for the crowd with both teams managing just one shot on target in 120 minutes.
Equatorial Guinea now face Sadio Mane-inspired Senegal, one of the title favourites, in Yaounde on Sunday for a place in the semi-finals of the flagship African tournament.
While Senegal will be hot favourites to advance, Equatorial Guinea beat them in the only previous Cup of Nations clash 10 years ago.
Ranked 114th in the world, the Equatoguineans have impressed throughout the tournament in their first appearance after qualifying, having previously competed as co-hosts and hosts.
Unlucky losers to the Ivory Coast, the National Thunder then ended the 35-match unbeaten run of Algeria before defeating Sierra Leone to finish group runners-up.
It was the second 0-0 draw on Wednesday with Egypt defeating the Ivory Coast 5-4 on penalties in Douala just before the Limbe match kicked off.
The players and match officials wore black armbands and observed a moment of silence before the kick-off in memory of the eight people who died in a stampede on Monday before Cameroon beat Comoros in Yaounde.
Mali had two Premier League players available and Brighton midfielder Yves Bissouma started while Southampton winger Moussa Djenepo sat on the bench and was introduced after 70 minutes.
Ibrahima Kone, who scored three of the four Mali goals in the group stage, fired just wide on seven minutes at the 20,000-seat Stade Omnisport, which overlooks the Gulf of Guinea.
Equatorial Guinea had a penalty appeal rejected after the referee checked the VAR monitor as a foul-riddled first half progressed.
The Equatoguineans were overly physical and Ivan Edu and Jose Miranda were yellow-carded before Mali wasted a half chance to end the deadlock.
A free-kick fell favourably for Amadou Haidara inside the box, but his timid shot was comfortably saved by Owono.
Veteran Mali coach Mohamed Magassouba looked on anxiously when Kone was injured, but the Norway-based forward was able to continue after lengthy treatment.
It was then the turn of Mali to appeal for a penalty when Moussa Doumbia fell as half-time approached, but the referee changed his decision to initially award a spot-kick after reviewing the incident.
A goalless opening half ended with a third yellow card to an Equatoguinean with Pablo Ganet the offender. His team committed 15 fouls during the half, but failed to get a single shot on target.
The best scoring chance so far came on 58 minutes when the perseverance of Bissouma set up Haidara, but he blazed over from close range.
As the match entered the final quarter of regular time, Mali continued to dominate possession, pass more accurately and concede far fewer fouls, but Equatorial Guinea held firm under pressure.
Djenepo enlivened the Mali attack, but could not force a breakthrough and after 95 goalless minutes, the final last-16 match went to extra time.
