Ali Al Habsi was in inspired form for the Gulf nation, which hit the crossbar late, in a game of several chances but wayward finishing.
With main Group A rival Australia securing all three points from its opening game against Kuwait on Friday, a win was vital for the South Koreans and they got it thanks to a goal in first-half stoppage time from Cho Young-Cheol.
Oman had several half chances throughout the match but failed to capitalize, with only some heroic goalkeeping from Ali Al Habsi and indecision in the final third from South Korea keeping the scoreline at 1-0.
A scrappy opening period gave way to an entertaining first half that was largely dominated by Uli Stielike's South Koreans, with Oman playing on the counter in front of 12,552 fans at Canberra Stadium.
Cho had Omani goalkeeper Ali Al Habsi worried early with a low drive from the edge of the area, and the Gulf side was lucky not to find itself behind a minute later when Son Heung-min hit the bar with a delicate chip.
Oman began to grow into the game and it was not long before it had a chance of its own, with Jaber Al Owaisi wasting a chance he should have taken when he put a free header over the bar in the 12th minute.
A penalty appeal for Oman was contentiously ignored after Kim Joo-Young clattered into Qasim Said in the 15th minute and there were signs of stress appearing across the South Korean back line.
An early injury to right back Kim Chang-Soo forced Stielike into a change, with veteran Cha Du-Ri replacing him.
Despite enjoying the majority of possession, South Korea struggled to find the killer ball in the final third in the face of a resolute and compact Omani defense.
Cha saw an errant shot fly wide from the edge of the box midway through the first half, while Son tested Al Habsi with a stinging free kick from 30 yards — but the veteran goalkeeper made an acrobatic stop.
South Korea finally broke the deadlock in the shadows of halftime when Al Habsi failed to hold onto a rasping drive from Koo Ja-cheol, allowing Cho to poke home the rebound from 6 yards.
Lee Chung-Yong ensured his side picked up where it left off in the second half, his left-footed drive from the edge of the box finding the side netting.
A vicious ball into the box from Park Joo-Ho presented South Korea with another chance to score in the 56th minute, but Koo's stinging header was brilliantly saved by Al Habsi at point-blank range.
South Korea missed yet another chance of its own with five minutes left when substitute Lee Jung-Hyup inexplicably elected to cross the ball when he was through on goal.
The South Koreans were nearly made to pay in injury time when Amad Al-Hosni saw his header acrobatically saved onto the bar by Kim Jin-Hyeon.
That was as close as the Omanis got to finding the back of the net, as South Korea held on for a vital 1-0 win that sees it go second in Group A, behind Australia on goal difference.