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The Azeris, who drew 0-0 with England in 2004, took the lead through Murad Aghakishiyev after 20 minutes.
But an under-strength Irish side, missing Bolton's Joey O'Brien and Man City's Stephen Ireland amongst others, fought back - with Keogh, earning his third U-21 cap, the star.
He hauled Ireland level after 58 minutes, then grabbed the winning goal two minutes from time.
Givens' side will play the second leg of the tie next Thursday at Kilkenny's Buckley Park, two days after Keogh celebrates his 20th birthday.