The Zimbabwean outfit went into Saturday's first-leg encounter with home advantage, but it was the Nigerian visitors who took the lead at the Barbourfields Stadium when Bernard Okorowanta opened the scoring shortly after half-time.
However, How Mine levelled the scoring on the hour mark thanks to Morris Kadzola's strike.
It looked as though the game would finish level, but Mupera kept his nerve from 12 yards in the third minute of injury time to give How Mine a lead to hold on to going into next week's return leg.
Malian side Djoliba were runners-up in 2012, but their hopes of reaching the group stages this year were dealt a huge blow with a 2-0 defeat against Wadi Degla of Egypt at the Cairo Military Academy Stadium.
After a goalless first half, the Egyptian side moved ahead in the 57th minute through Mostafa Talaat's strike, before an own goal from Abdoulaye Traore in injury time means that Djoliba have it all to do in the second leg.
Elsewhere, Jean Paul Niyonzima's solitary strike handed AS Kigali of Rwanda a 1-0 triumph over Morocco's Difaa El Jadida, while Tunisians Etoile Sahel also have a lead to take into the second leg after Alaya Brigui's eighth-minute goal ensured a 1-0 win over South African visitors SuperSport United.
