Nyora kupfuurira kweiyi ndima - Horowitz akanga ari mutambi anotungamirira muU.S. mukati mema1930 nama1940. Akanga ari U.S. Open Champion muna 1936, 1938, uye 1943. Muna 1941, akarasikirwa nomutambo (+0−3=13) naSamuel Reshevsky nokuda kweU.S. Chess Championship. Akatamba muU.S. Team muOlympiads ina dzeChess, muna 1931
Muna 1945, Horowitz akahwina mumwe wemakwikwi maviri chete eU.S. nekukunda GM Salo Flohr. Akagovana "mini-match" yake yemitambo miviri achipesana naFlohr, uye muchinyorwa cha1946 chechiitiko chimwe chete, akagovana mini-match yake achipesana naIsaac Boleslavsky.