Bulut was the star man for Fatih Terim's side as they cruised past Andorra to keep the pressure on Hungary, Romania and the Netherlands in Group D.
Burak Yilmaz and Arda Turan also found the net for Turkey, who ended a run of four games without a win with a superb performance.
Turkey's last victory before Friday's game came against Andorra back in March, and Terim will hope that this display will inspire them to better fortunes for the rest of campaign.
It was Bulut who provided the breakthrough, the Galatasaray striker meeting Gokhan Tore's right-wing cross to head into the bottom corner.
The 30-year-old doubled his tally just four minutes later with a spectacular goal as he found the net with a powerul right-footed effort from long range.
That goal effectively ended any hopes of an Andorra upset, but Terim's side refused to take their foot off the gas, midfielder Mehmet Topal smashing the crossbar after a quickly-taken free-kick.
Andorra managed to keep the deficit at two until the interval, but their respite was short-lived, Topal lashing wide following neat link-up play with Tore, before Yilmaz made it 3-0 as he tapped in Gokhan Gonul's right-wing cross after 64 minutes.
The win means that Turkey are three points behind Romania, who occupy the Group D play-off spot in second place, ahead of their meeting with Victor Piturca's men in Bucharest on Tuesday.
