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.
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(Reporting by Mark Gleeson, editing by Pritha Sarkar)
