 Zvinhu zvakachinja, uye kubva muna 2001 kusvika muna 2006, maTwins akaunganidza mwaka wakareba kwazvo wekukunda akateedzana kubvira paakatamira kuMinnesota, achienda 8577 muna 2001, 9467 muna 2002, 9072 muna 2003, 9270 muna 2004, 8379 muna 2005, uye 9666 muna 2006. Kubva muna 2002 kusvika muna 2004, Twins yakaunganidza yavo yakareba yakateedzana yeligi chikamu chemakwikwi akamboitika yapfuura yaive 1924 World Champion-1925 AL Champion Senators uye 196970 Twins. Yakatyisidzirwa nekuvharwa nekubatana kwechikwata pamwe chete neMontreal Expos muna 2002, timu yakarwira kuti isvike kuALCSvasati vabviswa 4-1 nevakakunda World Series yegore iroro Anaheim Angels. Kukunda kwavo mumakwikwi matatu akatevedzana, pamwe chete nemimwe mitambo yairwiwa zvakanyanya, kwakabatsira kugadzira kukwikwidzana kwakasimba neChicago White Sox mumakore achangopfuura, kutanga muna 2000 apo Sox yakabata chikamu paMetrodome, uye ichipisa kunyanya muna 2003, 2004, 2005 na2008. 