Vladimir Petkovic’s much-changed side were eager to end the group stage on a high, with their place in the last 16 already secured.
It took just 19 minutes for the Fennecs to assert their dominance, as Zineddine Belaid scored his first senior international goal with a terrific glancing header from Anis Hadj Moussa’s corner.
They doubled their lead six minutes later when Ibrahim Maza played in Fares Chaibi, who effortlessly cut his way into the box from the left and unleashed an unstoppable strike past Jesus Owono.
The Equatorial Guinea shot-stopper was beaten again by an Algeria side showing no mercy, after Maza headed home from Hadj Moussa’s cross to propel them into a 3-0 lead after 32 minutes.
Juan Micha’s men had a chance to reduce the deficit through Pablo Ganet, but Owono was then forced into a fine save to deny Monsef Bakrar at the end of a chastening first half.
Emilio Nsue was hoping to spark an unlikely comeback for Equatorial Guinea, as he cut Algeria’s lead to two with a superb angled right-footed strike which flew past Anthony Mandrea into the top left-hand corner.
It was the 36-year-old’s seventh goal at an AFCON finals, and he could have scored again moments later, but he was thwarted by Mandrea from close range.
That seemed to reignite an Algeria side, whose intensity had dropped off after the restart. Chaibi came agonisingly close to getting his second of the game when a neat piece of skill engineered a chance from inside the box, but his subsequent strike cannoned off the bar.
Ultimately, Petkovic’s men saw out the match with little fuss and will now prepare for a last-16 clash against the Democratic Republic of Congo when they return to Rabat next Tuesday.
Meanwhile, this first-ever AFCON group-stage exit will sting for the National Thunder, who have now only won two of their last 12 games (D3, L7).
Flashscore Man of the Match: Anis Hadj Moussa (Algeria)