Kuwait had started brightly and were the first to threaten after five minutes when Yaqoub Al Taher cut the ball back into the area from the byline but Walied Ali could only drive his shot wide of the post.
Odil Ahmedov then had a chance for Uzbekistan soon after but he contrived to head over the bar when found unmarked by Sanjar Tursunov six yards from goal.
But after that chances were at a premium and it seemed the game would remain goalless at half-time, only for Uzbekistan to claim the lead four minutes before the break courtesy of a deflected goal.
The Central Asians were awarded a free-kick just outside the area and Shatskikh drove an effort goalwards but the ball struck team-mate Haydarov to deflect beyond a bemused Nawaf Al Khaldi in the Kuwait goal.
Kuwait boss Goran Tufegdzic opted to change things around at half-time, bringing on Hamad Nayef, and the substitute made an almost immediate impression.
Nayef received the ball just inside the area and attempted to turn Anzur Ismailov, who hauled down the forward and the referee pointed to the spot. Al Mutawa stepped up to coolly convert the penalty.
The game opened up after that with both sides forging chances, but it was the Uzbeks who regained the lead in the 65th minute when Djeparov drove a powerful shot from outside the box into the back of the net.
Kuwait pushed for an equaliser in the closing stages and twice almost levelled through Ahmad Ajab and Yousef Naser, but Uzbekistan held firm to seal the win - and with it their place in the last eight.