Mertens had the visitors ahead just past the half hour mark but there was to be no repeat of the 8-1 hammering that Belgium handed Estonia in Brussels in November.
Mertens took advantage of a goalkeeping blunder to put Belgium ahead and Estonia suffered a further setback on the stroke of halftime when Artjom Dmitrijev was sent off for a studs-high challenge on Marouane Fellaini.
Estonia's stubborn defence prevented Belgium from finding the net until five minutes from the end when Chadli added a second.
Belgium have a four-point lead over second placed Greece in their qualifying group and are well placed to qualify for next year’s World Cup finals in Russia.
(Reporting by Mark Gleeson, editing by Pritha Sarkar)
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