Victory for Zimbabwe followed five consecutive draws in a mini-league completed by Malawi and top seeds Guinea, who will both be desperate for three points when they meet in Blantyre Tuesday.
Zimbabwe have eight points, Swaziland five and Malawi and Guinea two each with only the group winners guaranteed a place at the 2017 Cup of Nations in Gabon. The Warriors' biggest Cup of Nations qualifying victory was 5-0 against Seychelles and they beat Swaziland before, Eritrea and Malawi by four goals.
Swaziland, one of 16 countries never to feature at the biennial African tournament, suffered their third heaviest loss after 6-0 to Togo and 5-0 to Zambia. "What a wonderful day for the nation," Belgium-based striker Musona told reporters. "We won convincingly and are top of the table. "Our objective now must be to secure maximum points when Malawi come to Harare during June. I believe our chances of reaching Gabon are good."
Zimbabwe qualified for the African football showpiece in 2004 and 2006, winning once and losing twice in each tournament to make first-round exits.
Central African Republic, another of the 16 non-qualifiers, went top of Group B by coming from behind to edge Madagascar 2-1 in Bangui.
Malagasy Faneva Ima Randriatsima, who plays in the French second division, scored the only goal of the first half at Stade Barthelemy Boganda
Salif Keita levelled eight minutes after half-time and Kazakhstan-based Moussa Limane got the winner midway through the second half.
Central African Republic have seven points, 2015 Cup of Nations bronze medalists the Democratic Republic of Congo six, Angola four and Madagascar two.
Mali replaced Benin as Group C leaders after a late Mustapha Yatabare goal delivered a second 1-0 win over Equatorial Guinea in four days, this time away at the Nuevo Estadio de Malabo.
While Mali (10 points) and Benin (eight) are set to fight for first place, the Equatoguineans have just one point and cannot reach the finals after finishing fourth last year as hosts.
A Mohamed Zubya hat-trick helped Libya trounce Sao Tome e Principe 4-0 in a Group F match moved to Cairo because of post Moamer Kadhafi era lawlessness.