YOKOHAMA, Japan, Aug 3 (Reuters) - The Dominican Republic guaranteed themselves a shot at no less than playing for baseball"s Olympic bronze medal after eliminating Israel with a 7-6 win on Tuesday that featured a balk, a rare bunt double, three huge blasts and a highlight reel behind-the-back basket catch. In the end, the team representing one of the world"s most baseball-loving nations beat a thrown-together squad aspiring to drum up some semblance of interest in the sport back home through their first Olympic appearance. In a sign of both the hard-fought nature of the game and the spirit of the Olympics, both teams lined for hugs a few minutes after one grieved while the other rejoiced, a scene not common in baseball. And rival former Major Leaguers including Ian Kinsler of Israel and Dominican"s Melky Cabrera snapped photos together to recall the night. "They displayed and showed a lot of grit and courage," Dominican Republic"s hero of the game Jose Bautista said of the Israel squad. "They were down late, hit a crucial home run and put us against the wall." Both sides said they wanted to honor the others" efforts. Israel"s Danny Valencia held back tears afterwards. "It’s like our hearts were ripped out of us. Both teams wanted it bad," he said. "It’s going to take some time to get over. This hurts right now." Between them, the sides committed three costly errors, stifled at least four potential rallies with failed attempts at aggressive base running, and repeatedly pierced an empty stadium with profanities directed at the plate umpire"s balls-and-strikes calls. The strange game appeared to take its final turn when ex-big leaguer Valencia struck an eighth-inning two-run homer - his tournament-leading third - to grab a 6-5 lead. While rounding the bases, he turned toward his dugout and twice yelled "let"s go!" to his celebrating teammates. But Dominican Republic - spurred on by a team official defying the stadium"s noisemaker ban by scraping a merengue instrument known as a guira - would not let it end there. Johan Mieses took a pitch thrown to what he called his favorite spot and catapulted a home run metres shy of literally exiting the stadium to tie the game 6-6 in the bottom of the ninth. A single to left by former Toronto Blue Jays star Bautista later in the inning drove home the game-winning run. Bautista, who had no hits in the tournament before then, had entered the game due to a hamstring injury to center fielder Emilio Bonifacio. "It’s a great feeling coming through for the team in any situation, let alone to win the game in the last inning," Bautista said. "We were facing packing our bags and going home. Now, we’ll be playing in the medal round." Three games over the next two days among the remaining four teams will decide who will compete for which medals. Dominican Republic next face the United States on Wednesday with the loser heading to Saturday"s bronze-medal game. The winner of that contest takes on the losing side of Japan versus South Korea for a final chance at entering the gold-medal game instead of being relegated to the bronze match-up.