As well as needing to win in Cardiff, Robert Page's side were relying on Armenia taking points off Croatia, but neither occurred on a frustrating night.
Nico Williams's early opener was cancelled out by a controversial Yusuf Yazici penalty, while Croatia earned a 1-0 victory over Armenia.
The Dragons now drop into the playoffs, concluding the group with 12 points from eight matches and finishing four points adrift of Croatia.
Knowing that three points were imperative, Wales showed their intent from the off and took the lead as early as the seventh minute, Williams cutting inside before firing a shot inside the far post from 20 yards out.
That brilliantly-taken goal further lifted the mood inside the Cardiff City Stadium, their team responding with a performance that would have made new viewers to international football question how Turkey were sitting at the top of the group.
During what had quickly become a feisty opening 45 minutes, Wales were also denied what appeared a certain penalty, Samet Akaydin not being punished for bundling Brennan Johnson over in the penalty area.
Although Wales survived a let-off when Kerem Akturkoglu squandered an opportunity just before half time, Croatia went in front against Armenia to leaves Page's side needing things to turn back in their favour.
Page would have been happy with Wales' start to the second half but as the minutes ticked by, the temptation to sit deeper grew, and Turkey looked to capitalise.
As the game headed into the final quarter, the visitors got their equaliser from an extremely soft penalty decision, Ben Davies was adjudged to have upended Kenan Yildiz.
In comparison to the one that did not go Wales' way in the first half, it was harsh, yet Yazici converted from 12 yards to leave the home side needing a response.
Instead, Turkey looked the most likely winners, Yusuf Sari fizzing a shot marginally off target from distance, and it led to the introductions of Daniel James and Kieffer Moore from the substitutes' bench.
However, once the full-time whistle went in Zagreb, confirming a Croatia victory, Wales' playoff fate was sealed, and they will now look forward to Thursday's draw.