A third-minute goal from Pierre Webo broke the deadlock before Benjamin Moukandjo added a second on the half-hour mark with an individual goal.
He carved his way through three challenges before neatly slotting home.
Ahmed Akaichi's stunning left-footed volley in the 50th minute reduced the deficit to 2-1 and revived Tunisia's hopes of levelling the match and snatching qualification on the away goals rule after the sides drew 0-0 in last month's first leg.
A second Tunisia goal never materialised, however, as they retreated into a cautious approach.
Makoun restored the two-goal advantage with a near-post header from a corner midway through the second half which was followed by a terrible miss from Moukandjo.
Samuel Eto'o, playing on the right wing rather than his usual centre forward role, hit the upright and Makoun reacted quickest to tuck away the rebound for Cameroon's fourth three minutes from time.
They join the Ivory Coast and Nigeria, who both qualified on Saturday, as African representatives in Brazil with two more places to be decided on Tuesday.
Cameroon have now qualified for the World Cup finals for an African record seventh time. They were the first side from the continent to reach the quarter-finals when the tournament was staged in Italy in 1990.
(Reporting by Mark Gleeson; editing by Toby Davis)
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