Bulut struck twice in the first half and also netted after the break after Burak Yilmaz had netted Turkey's third goal. The hosts completed the scoring in injury time when Arda Turan headed their fifth to keep alive their hopes of reaching the global finals.
Turkey exerted all the early pressure, but Gokhan Tore was off target with a shot from 20 yards and then Andorra keeper Ferran Pol was well placed to beat away a shot from Yilmaz following a throw-in by Gokhan Gonul.
It took Andorra half an hour to create their first chance but Volkan Demirel punched away a corner by Marc Pujol Pons and Ivan Lorenzo Roncero fired the loose ball over the bar from 20 yards.
Turkey finally made their pressure tell with two goals inside the space of four minutes. Tore crossed from the right wing and Bulut headed the opening goal 34 minutes into the game.
Four minutes later the home side had doubled their lead as Bulut netted his second, firing home from long distance.
Turkey should have extended their lead just before half-time but Yilmaz headed over from close range following a Tore cross.
They increased their lead just after the hour when Yilmaz scored from close range from Gonul's pass and Bulut completed his hat-trick when he lobbed the keeper after 67 minutes.
Pol then saved brilliantly when he tipped Bulut's shot from inside the six-yard box around the post, and Pol again denied Bulut with eight minutes to go as Turkey went in search of a fifth goal.
It finally came when Turan headed into the roof of the net three minutes into added time.