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Famara Diedhiou opened the scoring for Senegal, who then conceded a surprise equaliser to Jannick Buyla, only for substitutes Cheikhou Kouyate and Ismaila Sarr to come on and restore Senegal's lead and put the result beyond doubt.
Diedhiou got on the end of a defence-splitting pass from Sadio Mane after 28 minutes, outsprinted the centre backs and hit home with a first-time effort with his left foot.
It looked as if it might open the floodgates in a mismatch between Africa's top-ranked team and an Equatorial Guinea side, who are 94 places beneath them in the FIFA rankings.
But Senegal were unable to add any more goals despite dominating the first half and then found themselves in a sticky situation five minutes after the resumption.
They had a penalty awarded against them when a pass from Iban Salvador struck captain Kalildou Koulibaly on the hand, but referee Victor Gomes changed his mind after reviewing his decision on the pitchside VAR screen.
Koulibaly was struck on the hand, but at close range and without his arm being away from his body.
Despite the disappointment of not getting a spotkick, Equatorial Guinea came storming forward and an interchange of passes on the edge of the area allowed Buyla to stab home a 57th-minute equaliser.
Yet parity lasted less than 10 minutes as Kouyate restored his side's lead, three minutes after coming on in the 65th minute.
A mix-up in the Equatorial Guinea defence saw the two centre backs challenge for the same high ball, spilling it backwards where Kouyate cleverly stole in and lifted his finish over goalkeeper Jesus Owono.
Senegal made sure of the result when Sarr had an easy tap-in in the 79th minute. He had come on for his first appearance of the tournament and immediately took hold of the ball, dominating the later stages of the contest.
It was his first game since he suffered a serious knee injury playing for Watford against Manchester United in November and his arrival at the tournament followed a tug-of-war over his availability between club and country.