Kammala jumla mai zuwa: Ibragimov ya raba wuri na farko tare da Vladimir Kramnik da Andrei Kharlov a 1991 USSR Under-26 Championship. An ba shi lambar yabo ta Grandmaster ta FIDE a 1993. Ibragimov ya lashe Chigorin Memorial a shekarar 1994 da Biel Masters Open a shekarar 1997. A shekara ta 2002 ya fara bugawa Amurka wasa, inda ya zauna a New Haven, Connecticut. Ya kasance abokin nasara a gasar US Open ta 2004 kuma ya raba matsayi na uku a gasar zakarun Amurka ta 2006. Ibragimov ya taka leda a tawagar Amurka da ta dauki lambar tagulla a gasar
Gasar Olympics ta Chess ta 2006.