Topal's second-half volley arrived after a barrage of attempts on goal by Mircea Lucescu's side, with Turkey beating Ireland for only the third time in 14 attempts.
Martin O'Neill's men would have hoped for a result and performance that would help to bury the memory of their 5-1 home defeat to Denmark in the World Cup qualifying group D play-off, but they found attacking opportunities few and far between in Antalya.
O'Neill handed debuts to Aston Villa's Scott Hogan and West Ham's Declan Rice, but they came up against a well-organised Turkey outfit who stayed on the front foot for much of the game.
The result and the generally positive nature of Turkey's performance will help Lucescu to rebuild morale after a home defeat to Albania last November and the disappointment of finishing fourth in their World Cup qualifying group.
Ireland goalkeeper Colin Doyle made his first save of the game after four minutes, gathering Yusuf Yazici's long-range shot as it bounced awkwardly towards the top corner of the net.
Turkey's pursuit of a spectacular opener did not end there and Doyle watched audacious efforts from long distance by Hasan Ali Kaldirim and Hakan Calhanoglu flash over the crossbar before the visitors mustered their first attack.
Ireland's first sight of goal arrived after 17 minutes when debutant Scott Hogan latched onto a brilliantly threaded pass by Jeff Hendrick but, in rounding goalkeeper Volkan Babacan, took the ball too far wide and could not find the angle with his shot, which hit the side-netting.
Cenk Tosun, in goalscoring form for Everton in the Premier League, rifled a low shot from just inside the box that Doyle got down well to save, and moments later Shane Duffy went close to scoring an own goal when he diverted Gokhan Gonul's cross just past the post with a backwards diving header.
The second half was only seven minutes old when Turkey captain Topal volleyed his side into the lead, losing his marker before connecting with Yazici's cross and beating Doyle from deep inside the area.
With Ireland beginning to tire, AC Milan's Calhanoglu darted across the edge of the visitors' penalty area and drilled a low shot towards goal that Doyle did well to parry and then grasp before the rebound went astray.
O'Neill sent on six substitutes in the last half an hour, but his blend of youth and experience could not force an equaliser on a humid night in Turkey.