The victory in Kinshasa left the Congolese with a virtually insurmountable lead, with Anderlecht striker Dieumerci Mbokani scoring twice and Deo Kanda and Issama Mpeko adding the others after a goalless first half.
It was the biggest win of the 15 final-round, first-leg qualifiers played across the continent at the weekend, and should send the Congolese, winners in 1968 and 1974, back to the finals after missing the last three tournaments.
Algeria enjoyed a 1-0 away win against Libya, played in neutral Casablanca, after substitute El Arbi Hillel Soudani scored two minutes from time, giving the visitors a massive advantage for the return leg.
Algeria's pressure paid off with a cleverly worked goal for the Portugal-based striker, who has now netted five in his seven international appearances.
However, the win was marred by a mass brawl on the pitch between the two sets of players at the final whistle.
Mozambique pulled off a surprise 2-0 home win over Morocco side to give themselves a good chance of making the finals.
The home side had been given little chance when the draw was made, but goals from Miro and Domingues ensured a defendable lead for next month's return match.
The result put further pressure on Morocco's Belgian coach Eric Gerets, already feeling the ire of the local media and fans after a disappointing start to 2014 World Cup qualification.
Zimbabwe, another neighbour of 2013 hosts South Africa, exceeded expectations by beating Angola 3-1, while Ibrahim Yattara scored the only goal as Guinea struggled to beat visiting Niger.