Koo struck either side of half-time as Cho Kwang-Rae's side, who are bidding to end a 51-year wait for Asian Cup glory, avenged their defeat at Bahrain's hands in the group phase of the 2007 tournament.
There was a tense finish to the game for the Koreans, however, with Faouzi Aaish netting from the penalty spot in the 85th minute after Kwak Tae-Hwi had been sent off for bringing down Abdulla Al-Dakeel inside the box.
Victory took the Koreans level on points with Australia at the top of Group C, but they endured a more awkward evening than the Socceroos had in their 4-0 demolition of India earlier in the day.
South Korea meet Australia on Friday in a match that seems destined to decide which of the two favourites finishes top of the pool, while Bahrain will bid to keep their hopes of a knockout round place alive by beating India.
South Korea may be accustomed to playing at sold-out arenas crammed with passionate fans in their homeland, but the official attendance at the 22,000-capacity stadium was less than 7,000.
The first half was similarly low-key, with South Korea occasionally imprecise in possession and 19-year-old striker Ji Dong-Won, replacing the injured Park Chu-Young, struggling to provide a cutting edge up front.
Manchester United star Park Ji-Sung twice went close, testing Mahmood Mansoor with a low shot and flashing a header wide, while Koo also brought a save from the Bahrain goalkeeper after jinking inside from the right.
The breakthrough came five minutes before half-time and, as with many of the goals in the competition to date, it owed more to luck than dead-eyed finishing.
A mis-hit shot by Ki Sung-Yueng arrived at the feet of 21-year-old Jeju United midfielder Koo, whose shot clipped the thigh of the sliding Abdulla Marzooqi and looped over a stranded Mansoor into the net.
The best Bahrain could offer in response was a pair of long-range free-kicks from Mahmood Abdulrahman that bounced into the clutches of South Korea goalkeeper Jung Sung-Ryong.
Koo completed his brace seven minutes into the second half, side-footing into an empty net from a matter of yards after Mansoor had done well to claw out a dipping effort from South Korea right-back Cha Du-Ri.
Their resolve broken, Bahrain began to leave gaps at the back and Cha almost made it 3-0 after striding into space on the right but his left-foot shot did not have sufficient curl to bend inside the left-hand post.
Kwak looked bemused as referee Abdullah Mohamed Al Hilali showed him the red card with five minutes to play, but he undoubtedly clipped Al Dakeel's heels as the substitute raced into the box.
Aaish calmly placed the penalty into the bottom-left corner, with Jung then called upon to tip a looping Abdulla Fatadi header over the bar as Bahrain pressed for an equaliser.