Mash'al Mubarek forward Kuziboyev's scrappy first-half equaliser cancelled out a header from captain Koo Ja-cheol as South Korea failed to repeat their Asian Cup quarter-final win over Uzbekistan back in January.
Uli Stielike's side needed extra-time to see off Uzbekistan in that last-eight encounter and they were once again unable to secure victory in 90 minutes.
Stielike would have seen plenty of room for improvement in South Korea's first game since their Asian Cup final defeat against Australia as he selected an experimental side.
Lee Jae-sung made his senior South Korea debut, while QPR defender Yoon Suk-young started after missing the Asian Cup and Kim Bo-kyung made his first international appearance since the World Cup.
Son Heung-min scored both goals in South Korea's 2-0 victory over Uzbekistan in Melbourne and the winger turned provider for the opening goal 15 minutes in.
The Bayer Leverkusen man's inviting corner from the left was met by Koo, who planted a header into the back of the net from inside the six-yard box.
Koo had an opportunity to double his tally nine minutes later, but this time header over the crossbar with goalkeeper Eldorbek Suyunov stranded.
Uzbekistan also posed a threat going forward and they were level on the half-hour mark courtesy of a somewhat fortunate goal from Kuziboyev.
Sardor Rashidov's heavy touch looked to have wasted a golden opportunity to equalise, but his cross from the byline struck Kuziboyev and then Kim Ki-hee, who was unable to prevent the ball from crossing the line.
The hosts lost Lee Jung-hyub and Jeong Dong-ho to injury before half-time and they could have been behind at the break, but Rashidov's effort was wide of the far post.
Son fired a free-kick over the crossbar nine minutes into the second half as South Korea looked to restore their advantage, but they continued to look vulnerable at the back.
Lutfulla Turayev's strike from 20 yards out was palmed away by a diving Kim Seung-gyu midway through the second half as Uzbekistan strived to gain revenge for their Asian Cup defeat.
Koo thought he had won it 18 minutes from time, but he was flagged for offside as Stielike's men had to settle for a draw.
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.