With the hosts having already qualified for the World Cup finals in Germany next summer, the pressure was on Turkey to keep pace with rivals Greece, who had leapfrogged Fatih Terim's side earlier in the day with a 2-1 win over Kazakhstan.
And in a scrappy game bereft of many clear-cut opportunities, Besiktas midfielder Tumer struck the winner in the 55th minute to put the Turks two points above Greece in the standings.
With just one game left in qualifying - away in Albania next month - Turkey now have a decent chance of claiming second place and a spot in the play-offs.
Ukraine had the first real chance of the game after a quarter of an hour but Anatoli Tymoschuk could only sky his shot over the bar.
Turkey, who finished third in the 2002 World Cup, finally got into the game and had two efforts within a matter of minutes.
First Fatih Tekke saw his well-struck shot blocked by Andriy Rusol in the six-yard box before midfielder Gokdeniz Karadeniz powered a strong drive straight into the chest of Olexandr Shovkovskiy.
In the only other clear opportunity of the first half, Karadeniz again shot too close to Shovkovskiy when well placed inside the area.
The second period was certainly much more open and the first goal duly arrived 10 minutes after the half-time interval when Metin beat three defenders and crashed a superb shot into the top corner past Shovkovskiy.
The Ukrainians, without talismanic AC Milan striker Andriy Shevchenko to lead the line, went on the offensive in search of the equaliser but found away goalkeeper Volkan Demirel in sharp form.
Arguably their best chance fell to Oleh Husev in the 75th minute but he found the side-netting from just inside the area.
The dying stages were dominated by the hosts, but stubborn defending - with Kaiserslautern's Alpay Ozalan particularly impressive at the heart of the backline - saw Turkey home.
Ukraine: Shovkovskyi, Federov, Vaschuk, Rusol, Nesmachnyi, Tymoschuk, Husev, Rotan (Venhlinskyy 68), Shelayev (Rebrov 79), Voronin (Gusin 84), Belyk.
Subs Not Used: Startsev, Radchenko, Nazarenko, Rykun.
Booked: Husev, Nesmachnyi.
Turkey: Demirel, Hamit Altintop, Toraman, Ozat, Sahin, Alpay, Buruk (Akin 87), Metin, Karadeniz (Cimsir 46), Tekke, Sukur.
Subs Not Used: Ongun, Akyel, Seyhan, Halil Altintop, Sas.
Booked: Hamit Altintop, Buruk.
Goals: Metin 55.
Ref: Alain Sars (France).