Juventus midfielder Ramsey had already missed two golden chances before he opened the scoring, while Gareth Bale blazed a second-half penalty over, but Turkey failed to make Wales pay for their profligacy and Roberts added a second deep into stoppage time to seal it.
After their opening game draw with Switzerland, Robert Page’s side now sit on four points, a tally which will almost certainly be good enough for one of the best third-placed finisher slots at the least, with a Group A meeting with Italy in Rome still to come in their final fixture.
Page named an identical side to the one that had started the Switzerland game, but his players responded with a far more positive, assertive performance.
Bale twice created wonderful openings for Ramsey, the former Arsenal man first denied by UÄurcan ÇakÄ±r at the near post and then blazing over when breaking the offside trap.
The goal finally arrived shortly before the interval as Ramsey chested Bale’s sublime ball in behind and steered his finish beyond Cakir.
Bale had the chance to secure victory from 12 yards after being fouled by Mehmet Zeki Çelik but the Real Madrid man sent his spot-kick way over the bar.
He made amends during the fifth minute of added time, though, dribbling along the byline from a corner - with the Turks expecting Wales to try and keep the ball to run the clock down - and teeing up Roberts to stroke home.