Captain Chris Katongo scored with a deflected shot after 15 minutes to ensure home success after a week of snipping between officials and the team coach in the wake of their loss in Sudan last weekend.
Katongo's goal marked a successful opening of the new 40,000-capacity Chinese-built stadium on Zambia's copperbelt and will go a long way to easing tensions after the 2-0 defeat in Khartoum in their opening Group D game.
Zambia's flamboyant French coach Herve Renard criticised sports ministry officials for botching travel arrangements to Sudan, which he blamed for the defeat, and then revealed he had not been paid for the last six months since Zambia won the Nations Cup in February.
He has a contract with government rather than the football association and was told to temper his criticism by irritated officials.
The row over-shadowed the build-up to Saturday's game against a weakened Ghana side, without many of the key players who helped them to a World Cup quarter-final at the 2010 finals in South Africa.
But Ghana, who Zambia also beat in last February's Nations Cup semi-final, started the World Cup qualifiers with a one-sided 7-0 win over Lesotho on June 1.
Morocco substitute Hamza Abdourazzouk scored a dramatic equaliser one minute from time to earn a 2-2 draw with top-ranked Ivory Coast.
A delicate chip from Salomon Kalou and a stooping header by Kolo Toure had looked set to ensure a second victory for the Ivorians in Group C.
Kalou chipped the Ivorians into an eighth-minute lead, outsprinting the defence to get on the end of a fine through ball from Siaka Tiene.
Captain Houcine Kharja equalised for Morocco from the penalty spot but Toure put the visitors back in front with a close-range header on the hour.
It was the Manchester City defender's fourth goal for his country on his 98th appearance for the Elephants.
Talismanic captain Didier Drogba, who scored last week when the Ivorians launched their campaign with a 2-0 home win over Tanzania, was a towering presence in attack before being taken off with six minutes left.
Abdourazzouk then grabbed the equaliser with a powerful header, much to the relief of Morocco's Belgian coach Eric Gerets.