Ryan Lavarnway homered twice for Israel, which made its Olympic baseball debut, and Ian Kinsler also went deep.
Lavarnway tied the score 5-5 against former big league reliever Seunghwan Oh (1-0) in the ninth inning with his second home run of the game.
Under international rules, extra innings start with runners on first and second, an even bigger distortion than the controversial major league runner on second rule used during the pandemic in 2020 and this season.
Kinsler took a called third strike that ended the top of the 10th against Seunghwan Oh (1-0), who struck out the side to give four South Korean pitchers 17 strikeouts.
Jaegyun Hwang sacrificed starting the bottom half, and Ji Hwan Oh popped out to Ty Kelly, who made an over-the-shoulder catch in short left field.
Bleich (0-1), whose big league career consisted of two games for Oakland in 2018, hit Kyoungmin Hur on the rear, then brushed the jersey of Euiji Yang with his next pitch.
Kinsler's two-run homer in the third off Taein Won and Lavarnway's two-run drive in the sixth against Wonjoon Choi built a 4-2 Israel lead.
Ji Hwan Oh tied the score 2-all with a two-run homer off Jake Fishman in the fourth, and June Hoo Lee and Hyunsoo Kim hit consecutive home runs in the seventh that tied the score off Zack Weiss, a 29-year-old right-hander whose big league career lasted four batters for Cincinnati on April 12, 2018.
Ji Hwan Oh''s RBI double, his third hit of the game, put South Korea ahead 5-4 in the three-run seventh, but Lavarnway homered off Oh in the ninth on a pitch nearly shoulder high.
Lavarnway was 3 for 11 for Cleveland in June while Austin Hedges was on the concussion injured list.
The United States opens Group B on Friday against Israel (0-1) and plays South Korea (1-0) on Sunday.
Unlike most Olympic sports that feature top athletes, the baseball tournament mostly serves as a showcase for players trying to get signed for major league stretch runs and minor league prospects not near the top of their organization depth chart.
Japan does have most of its top players after the Central and Pacific Leagues stopped their season for the Tokyo Games.
Israel starter Jon Moscot lasted nine pitches, giving up a leadoff single to Hae Min Park. With a 2-2 count on Lee, the 29-year-old right-hander stepped off and an athletic trainer came to the mound.
Moscot tried a warmup pitch, winced and hopped off. Moscot made eight appearances with Cincinnati in 2015-16 before Tommy John surgery.
He was replaced by Fishman, a 26-year-old left-hander taken by Miami from Toronto in the Triple-A phase of last year's winter meeting draft.