Aaron Ramsey and Connor Roberts scored at the end of each half to secure a 2-0 win and take Wales on to four points from two games.
Skipper Bale also missed a penalty with the score at 1-0 - a wild effort which he later apologised to his teammates for - as Wales now focus on their final Group A fixture against Italy in Rome on Sunday.
No team failed to make the last 16 at Euro 2016 in France having accumulated four points - and Bale was confident about making the knockout phase after this win.
“We’re in a fantastic position now,” Bale said after Wales had built on their opening draw against Switzerland.
“If you’d offered us four points after the first two games before the tournament started we definitely would have taken it.
“We’ve got one more game to go and it will be difficult. It’s a very difficult group.
“We are going to enjoy this victory for a day or so, get our recovery in, and look forward to Italy.”
Bale led Wales’ post-match huddle celebrations and apologised for his wayward spot-kick on the hour.
The Real Madrid forward has not scored for Wales since October 2019 and passed up the opportunity after he himself had been tripped just inside the area, blasting his effort over the crossbar.
“I just got under the ball too much,” said Bale, who had assists for both goals and created five big chances in the contest, more than any team in a single game at Euro 2020.
“It’s one of those things that happens in football and it’s not a nice feeling.
“But I felt I showed good character to keep going.
“I’m experienced enough to keep going and not let it affect me too much, and I showed that with the second assist at the end.
“It (the huddle) is something we do after the game. I made a funny joke for apologising for missing the penalty.
“After that we had a good chat because it’s nice for the players and backroom staff, who work so hard, to be involved.”
Turkey’s second defeat of the competition leaves them with an uphill battle to qualify for the round of 16.
Senol Gunes’ exciting young side were considered as dark horses to win the tournament before a ball was kicked after taking four points from world champions France in Euro 2020 qualifying.
But nothing other than victory over Switzerland will give them a shot of making the knockout stage.
Veteran boss Gunes said: “Qualification was a dream for us, but it is difficult now.
“We just lost the ball on too many occasions and could not develop a clear attacking strategy.
“The players are responsible for their roles. I am responsible for the results.
“I tried to put the best players on the pitch and I know this team can play much better than this.
“But the rival was much more balanced and tried to control us.”