Miroslav Blazevic's side had won the first meeting between the sides 7-0 last September but they were made to work harder for victory this time around in Tallinn.
A cagey opening was played in an unusual atmosphere as the away fans remained quiet for 24 minutes to remember Sarajevo fan Vedran Puljic, 24, who was killed in violence ahead of his team's match at Siroki Brijeg in the domestic league on Sunday.
Dzeko was off target with an early chance and was then denied by Estonia keeper Sergei Pareiko, while several deliveries narrowly eluded the visiting strikeforce, before the travelling crowd freed their voices.
And, suitably inspired, they took the lead on the half-hour mark as the VfL Wolfsburg frontman met a cross from the left to head home.
Vladimir Voskoboinikov fired wide when handed a chance to equalise by an error in the Bosnian defence three minutes before the interval.
Sander Puri then fired over for the hosts before Ibisevic made the game safe in the 64th minute.
A superb counter-attack ended with the Hoffenheim striker being played in behind the home defence, and he rounded Pareiko and slotted the ball into an empty net.
Shambolic defending from the hosts left Senijad Ibricic with a good chance in the closing moments, but the Hajduk Split winger was unable to capitalise and fired narrowly wide.
Nonetheless, a sixth victory in the group left Blazevic's men on 19 points and ensured Turkey would be unable to deny them a shot at reaching the finals via November's play-offs, regardless of their result against Belgium later in the evening.
That took the pressure off Bosnia's final match against Spain - already confirmed as group winners with a 100% record from their nine games - on Wednesday.
Estonia remain in fifth place, ahead of only Armenia, and will face the Belgians in midweek.