The dominant home team were struggling to penetrate resolute opponents in Yaounde when they were awarded a free-kick close to the touchline about 30 metres from the Zimbabwe goal.
As the set-piece was floated into the six-yard box, goalkeeper Ariel Sibanda failed to grasp the ball and it broke loose to Banga who, with his back to the goal, scored via a spectacular bicycle kick.
Banga was an unlikely 72nd-minute match-winner as he lined up as a centre-back in a 4-2-3-1 formation in front of a socially distanced crowd that included FIFA president Gianni Infantino.
While Zimbabwe rarely threatened to score in a physical Group A clash, Cameroon showed neat touches when building attacks at the Stade Ahmadou Ahidjo only to be let down by wild shooting.
Once ahead, the hosts felt sufficiently confident in their ability to retain the lead that they took off captain and vastly experienced attacker Jacques Zoua.
After launching his professional career with Coton Sport in northwestern Cameroon city Garoua, he played in Switzerland, Germany, Turkey, France, Belgium and Romania before returning to central Africa.
In the other Group A match, a looping header on 70 minutes from Siaka Bagayoko after a corner gave Mali a 1-0 win over Burkina Faso.
The two matches marked the start of the first football tournament in Africa since the coronavirus pandemic wreaked havoc from early last year.
Original hosts Ethiopia fell behind with preparations so the championship restricted to footballers playing in their country of birth was switched to Cameroon, then postponed twice as Covid-19 spread.
Cameroon officials said attendances would be restricted to 25 percent of the stadium capacity during the 12-day group phase, but may increase for the knockout phase.
Apart from Yaounde, matches will be staged at two venues in the commercial capital, Douala, and one in nearby Limbe.
On Sunday in Group B, the Democratic Republic of Congo, the only country to win the Nations Championship twice, tackle neighbours Congo Brazzaville, much the smaller of the two countries in size and population.
The Leopards of DR Congo and the Red Devils of Congo have met six times in CHAN qualifying, with two wins each and two draws, but never at the finals.