Ilyasova topped the Turkish scoring with 23 points and eight rebounds, while Hedo Turkoglu finished with 11 points and eight boards.
Maciej Lampe led the Polish side with 17 points and four rebounds despite foul trouble, with David Logan adding 13 in 25 seconds short of 40 minutes action.
Adam Wojcik opened the scoring for Poland with Turkoglu quickly replying, but another five Wojcik points saw Poland take a 9-4 lead after four minutes.
Lampe added another trey to give the Poles an 11-4 lead at the midway stage and with David Logan adding four points, Turkey took a timeout with 3:16 on the clock and the Poles 15-6 ahead.
Turkey did manage to cut the deficit, but a Lampe trey sent Poland into the first break 22-12 ahead.
Turkey forced a turnover in the first possession of the second period, and Szymon Szewczyk converted an alley-oop to increase his side's lead before hitting a trey to make it a 27-15 game.
A long Baris Hersek two kept Turkey in the game, but two lay-ups from Lampe - the second of which saw him add the bonus - put Poland 32-17 ahead.
Turkoglu trimmed that lead to 13 but Semih Erden wasted a pair of free-throws, as Poland led 32-19 at the midway stage of the period.
Roared on by their noisy support, Turkey responded with a 6-0 run capped by a pair of Turkoglu free-throws to make it a seven point game before Logan broke the tear.
That lead was narrowed to six as Ilyasova scored while being fouled, forcing a Poland timeout, and he drained the bonus coming out of the break to make it 34-29 - only to see Lampe drain a three just before the buzzer to send his side into the locker room 37-29 ahead.
Oguz Savas opened the scoring for Turkey to make it a six point game, but Wojcik replied at the other end.
Krzysztof Szubarga made it a double digit margin again with a score from the Land of Plenty, but Turkoglu cut the deficit with a pair from the line, and Lampe was forced to sit down on four fouls.
A spin move from Erden saw Turkey move within five points at the midway stage of the quarter, but Poland recovered to regain the initiative with a Wojcik basket and a pair of Szewczyk free-throws.
Bekir Yarangüme cut the lead back to 47-42 with 47 seconds of the period left when he hit a pair of free-throws., but Logan took his tally to eight with a lay-up, and Poland went into the final break with a 49-42 lead.
Ilyasova scored from outside the arc to make it a four point game with the first score of the fourth period, only to Lampe keep his side in front with his 17th point of the night.
Logan and Ilyasova exchanged baskets as the Poles remained three ahead, before Asik scored a put-back followed by a Poland turnover to force them into a timeout as their lead was trimmed to 53-52 with 5:53 on the clock.
Ilyasova tied the game at 53 with five minutes remaining before the same player drained a three to give the Turks their first lead of the afternoon. Turkoglu then slammed home to put his side 58-5320with 4:08 left, forcing another Poland timeout.
Poland weren't finished though, and Logan sunk a huge three to take the margin back to two. However, Ilyasova took his tally to 19 with a hook shot, and Lampe fouled out with 2:04 on the clock.
Turkoglu hit one of the resulting free throws, but Asik grabbed the rebound and - almost inevitably - Ilyasova netted to put his side 63-56 ahead.
Asik proved the punctuation mark with a jam before hitting one from two at the foul line to give his side a double digit lead and seal the win and the tournament title.
