The hosts should have had much more for their efforts in a game they completely dominated but they at least put last week's loss in the Netherlands firmly behind them. Estonia, also looking to bounce back from a defeat, showed some life early on with Joel Lindpere hitting the post.
But the game's critical moment came in the 19th minute when Jaager was dismissed for a professional foul on Burak Yilmaz.
By then Turkey had already gone close with Bulut heading wide, Yilmaz both missing the target and testing goalkeeper Sergei Pareiko and Arda Turan shooting over. That dominance continued as Pareiko again saved from Yilmaz, Mehmet Topal fired wide and Emre stretched the keeper from a free-kick.
Bulut headed over and Topal and Emre were also off-target with shots before the opener finally came on the stroke of half-time. Emre this time finished from 12 yards and Turkey powered on after the break with Bulut and Yilmaz again close before the second came on the hour.
Bulut was finally rewarded for his efforts with a good close-range header from a Sercan Sararer cross and Inan struck from the edge of the box 15 minutes later.
Turkey wanted another and Pareiko was kept busy to the end but there were to be no more goals.