Uzbekistan comfortably had the better of the game at a rain-sodden ANZ Stadium, but struggled to penetrate a resolute Korean defence for large parts.
Timur Kapadze was a menacing figure breaking from midfield for the Uzbeks and hit the post with a first-half header as well as going close after the interval.
Much of Korea's sights of goal came on the counter-attack but they were routinely let down by the final ball in ever-worsening conditions.
And the Uzbeks finally grabbed the goal they deserved after the hour as Sergeev's powerful header beat Korean goalkeeper Ri Myong-guk.
The 21-year-old's fourth goal in his last five competitive outings for Uzbekistan was ultimately enough, though a better touch in front of goal will likely be required in their following Group B games against China and Saudi Arabia.
Uzbekistan dominated possession throughout and Odil Ahmedov made his early intentions known with a fizzing 25-yard drive that flew wide.
Mirjalol Qosimov's men found joy time and again from their right flank, and one such charge resulted in an accurate ball onto Kapadze's head, but the 112-cap veteran's effort deflected off his covering defender and onto the post.
The heavens opened after the half-hour with Korea well regimented against a series of inventive Uzbek set-pieces which came to nothing.
Uzbekistan picked up where they left off into the second half as the rain intensified to make the pitch tougher to play, Kapadze's flick from a driven free-kick just looping over the crossbar.
The pressure began to build and Ri had to be alert soon after to tip Sanzhar Tursunov's teasing delivery from the right away with Ahmedov and Uzbek captain Server Djeparov just unable to convert.
And the pressure told in the 61st minute as Djeparov lofted an inviting ball into the path of an onrushing Sergeev, who met the ball firmly to send it back across goal, beyond Ri and into the corner.
North Korea were cautious in their attempts to get back into the contest with regular long balls up to lone frontman Pak Song-choi often failing to stick.
Uzbekistan should have doubled their lead late on and goalkeeper Ignatiy Nesterov incredibly preserved the points for his side with a stunning stop to deny a bullet header from Pak in the final action of the game.
