Cho Young-Cheol's strike on the stroke of half-time proved decisive in a largely unconvincing peformance from the side which Australia will seek to usurp to top the group it already leads on goal difference after its 4-1 win over Kuwait.
The Taeguk Warriors coach Uli Stielike was happy with his side's performance, arguing the Reds would rather build through the tournament than dazzle with a big win first up.
"I prefer to go into a tournament with a performance like today," the German said. "You learn from mistakes and get better as you go along.
"This is (better) than to start with a brilliant game leaving 5-0 and everybody thinks you already win the cup and after you get lesser and smaller and smaller."
With less than three days to go before the Reds take on Kuwait, Stielike's biggest concern was his two injured players - Kim Changsoo and Lee Chung Yong.
Oman coach Paul Le Guen was left to rue what he thought was a clear penalty in the first half.
Striker Qasim Saeed looked to have been scythed down in the box but New Zealand official Peter O'Leary did not order a spot kick.
"It was a 100 per cent penalty," Le Guen said. "It was a very, very bad decision. The game could have been different."
Oman plays the Socceroos on Tuesday and Le Gruen concedes it will be difficult.
"It will be tough for many reasons, but we will fight," he said.
Korea Republic made all the early running in front of a crowd of 12,552 and Koo Ja-Cheol tested Oman keeper Ali Al Habsi with a sixth minute snap shot as it searched for a quick breakthrough against a team with only one Asian Cup win in its history and just two wins in its last 12 internationals.
The highly rated Koreans, out to top the group ahead of Australia, came even closer three minutes later when Son Heung-min clipped the crossbar with a clever flick.
But the Omanis got a foothold in the match with Le Guen's men stemming the Korea threat with some neat approach play showing it also meant business.
And the frustration began to build for Stielike's side as its distribution lost its direction as the match wore on and Oman's confidence grew.
Midfielder Eid Al-Farsi had the chance to fire his team into a shock 40th minute lead when he bent a free-kick from the edge of the area just too high.
It took a flying 43rd-minute stop from Wigan back-up keeper Al Habsi to save Abdul Salam from the embarrassment of an own goal as his misplaced header looped towards the top right-hand corner.
But he was less effective on the stroke of half-time, only able to parry Ja-Cheol's shot into the path of Young-Cheol who slid the loose ball under the keeper's diving body for the game's sole goal.
The Koreans looked more polished after the break and Ja-Cheol's 58th minute header after a flowing move forced a superb save from Al Habsi to keep his side in the contest.
But for Al Habsi it would have been a far more comfortable margin for the Koreans who will nonetheless be pleased to have picked up three points to keep the pressure on Australia.
The Reds had a late escape when Al-Farsi's header from a stoppage time corner forced keeper Kim Jin-hyeon tip the ball onto the crossbar.