Serbia-based strikers Prince Tagoe and Dominic Adiyiah scored in the first half for the 2010 World Cup South Africa™ quarter-finalists and on-loan Sunderland midfielder Sulley Muntari added a third goal just before full-time.
Asamoah Gyan missed the Brazzaville match due to suspension, leaving replacement Tagoe to make the most of his chance by opening the scoring before Partizan Belgrade team-mate Adiyiah added a second just before half-time.
Few teams enjoy tackling a Congolese side starring Blackburn Rovers defender Christopher Samba in their backyard, but Ghana the exception, have won two previous Africa Cup of Nations qualifiers there.
The Black Stars climbed to seven points from three Group I outings, but Sudan remained hot on their heels thanks to a 3-0 triumph over Swaziland in Omdurman with Mohammed Bisha scoring in each half before Mohammed al-Tahir scored in the final minute.
Ghana and Sudan have accumulated seven points each with the former topping the table because they have scored one goal more.
The Chelsea striker cancelled out Seidah Tchomogo's opener and then grabbed the winner after latching on to a pass from Kader Keita as the Elephants maintained their secured their third win in as many games. The Ivory Coast are now five points clear of Benin at the top of Group H.
Zambia move clear
Zambia moved two points clear of Libya in Group C with a 2-0 victory over Mozambique thanks to goals from James Chamanga and Emmanuel Mayuka before a capacity 30,000 crowd at Machava Stadium in Maputo.
China-based Chamanga pushed Chipolopolo ahead just 11 minutes into the first half and Mayuka put the outcome beyond doubt with a stoppage-time goal.
"When my players want to win there is no stopping them. This was a great result and made up for the loss in Libya last year," said Zambia coach Dario Bonetti.
Dutch coach Mart Nooij, who came close to losing his job after a poor showing at the 2010 CAF Africa Cup of Nations in Angola, said Mozambique had inferior strikers to Zambia.
"We tried so hard to score without success and now the squad must prepare for the return match in Lusaka in June, which I believe will be a little easier because there will be more room to attack."
Congo DR pushed four-time African champions Cameroon down to third place in Group E after a comfortable 3-0 victory over Mauritius in Kinshasa. Recalled Tresor Lualua and Yves Ilunga converted penalty kicks and Matumona Zola was also on target for the Congolese.
Nigeria pressures Guinea
Guinea lost their 100 per cent Group B record, but stayed on top after coming from behind to draw 1-1 with ten-man Madagascar in Antananarivo where an early Yvan Rajaonarimana goal was cancelled by Djoulde Bah with ten minutes to go.
Nigeria moved to within a point of Guinea at the top of Group B thanks to a convincing 4-0 win over Ethiopia. Peter Utaka put the Super Eagles ahead inside the first minute and the Odense striker doubled his side's advantage before two late Ikechukwu Uche goals completed the rout.
Niger closed the gap on Group C pacesetters South Africa to a single point by coming from behind in Niamey to defeat Sierra Leone 3-1 in a West Africa showdown.