Former Real Madrid striker Balboa was sent clear by an incisive pass from substitute Daniel Ekedo and side-footed a curling shot past goalkeeper Samir Aboud to spark wild celebrations at the end of the Group A tie.
Equatorial Guinea, making their debut in the finals and starting the match with 11 players who were born abroad, had a first-half goal by Ivan Bolado controversially ruled out for offside after the ball slipped through Aboud's arms.
In the late match, Group A favourites Senegal slumped to a 2-1 defeat at the hands of Zambia.
Libya, who qualified for the finals despite the on-going conflict in their country, enjoyed plenty of possession but always looked vulnerable on the counter-attack.
The game started seven minutes late following the opening ceremony and a speech by President Teodoro Nguema Obiang Mbasogo which lasted several minutes while the teams were lined up and ready for kick-off.
Equatorial Guinea took the field with five players born in Spain, two in Ivory Coast and one each from Cameroon, Liberia, Cape Verde and Brazil.
Some qualified through parentage while others were naturalised, arousing debate over whether they had lived in the country for five years as required by the rules of football's governing body FIFA.
Equatorial Guinea are also coached by a Brazilian, Gilson Paulo, who was facing compatriot Marco Paqueta on Saturday.
The home team, co-hosting the finals with Gabon, were disappointed to have their first-half 'goal' chalked off and went close again when Juvenal Edjogo volleyed wide from an inviting position.
Ihab Albusaifi then tested home goalkeeper Danilo with a powerful volley during a spell of Libyan dominance but Equatorial Guinea continued to look dangerous.
Lawrence Doe almost broke through with a rasping free-kick stopped by Aboud.
With four minutes left Ekedo split the Libya defence and Balboa delivered the knockout punch.
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