Okan Yilmaz's late goal had seemed to have given Turkey a morale-boosting win, but Dunne popped up two minutes into stoppage time to fire home following a goalmouth scramble.
The game would have made interesting watching for England scout Nigel Pearson ahead of the make-or-break qualifier next month in Turkey between the two sides with the visitors fielding a strong starting line-up, including seven of those who played in the first meeting between the sides earlier this year.
The visitors dominated the opening proceedings opening up the home side almost every time they attacked with Tuncay catching the eye, but they failed to test Nick Colgan in Ireland's goal sufficiently.
They were made to pay for their prolificacy after 35 minutes with David Connolly capitalising on some slopping defending from Alpay to fire Ireland in front with his ninth international goal.
Ireland almost doubled the lead two minutes later with Gary Doherty forcing Rustu into a fine save low down to his near post after another mistake from Alpay and from the resulting corner Damien Duff saw his volley from the edge of the box pushed away by Rustu.
Turkey drew level seven minutes after the break with Hakan Sukur heading home Ergun's cross at the near post following another fine passing move by the visitors.
The visitors suffered an injury worry ahead of next month's game with England with Rustu limping off with a knee problem on the hour mark after mis-kicking a clearance.
His replacement Omer Catkic enjoyed a lucky break two minutes later when he misjudged Ian Harte's cross and was fortunate to see it slip out of his hands and onto the post.
Turkey went in front five minutes from time with Yilmaz getting on the end of Ergun's inviting left-wing cross to sweep the ball past substitute goalkeeper Joe Murphy.
Ireland refused to give in and drew level deep into injury time with Dunne sweeping home after Turkey failed to clear Stephen Carr's corner properly to make sure they do not go into next month's crucial game in Switzerland with a defeat hanging over them.
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